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Eric T Sawyer - One of the best experts on this subject based on the ideXlab platform.
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the corona theorem for the drury arveson Hardy Space and other holomorphic besov sobolev Spaces on the unit ball in c n
Analysis & PDE, 2011Co-Authors: şerban Costea, Eric T Sawyer, Brett D WickAbstract:We prove that the multiplier algebra of the Drury-Arveson Hardy Space H-n(2) on the unit ball in C-n has no corona in its maximal ideal Space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach Space result: the Besov-Sobolev Space B-p(sigma) has the "baby corona property" for all sigma >= 0 and 1 < p < infinity. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.
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function Spaces related to the dirichlet Space
arXiv: Complex Variables, 2008Co-Authors: Nicola Arcozzi, Eric T Sawyer, Richard Rochberg, Brett D WickAbstract:We present results about Spaces of holomorphic functions associated to the classical Dirichlet Space. The Spaces we consider have roles similar to the roles of $H^{1}$ and $BMO$ in the Hardy Space theory and we emphasize those analogies.
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the corona theorem for the drury arveson Hardy Space and other holomorphic besov sobolev Spaces on the unit ball in mathbb c n
arXiv: Complex Variables, 2008Co-Authors: şerban Costea, Eric T Sawyer, Brett D WickAbstract:We prove that the multiplier algebra of the Drury-Arveson Hardy Space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal Space, thus generalizing the famous Corona Theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach Space result: the Besov-Sobolev Space $B_{p}^{\sigma}$ has the "baby corona property" for all $\sigma \geq 0$ and $1
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carleson measures for the drury arveson Hardy Space and other besov sobolev Spaces on complex balls
Advances in Mathematics, 2008Co-Authors: Nicola Arcozzi, Richard Rochberg, Eric T SawyerAbstract:For 0s<1/2 we characterize Carleson measures µ for the analytic Besov�Sobolev Spaces on the unit ball in by the discrete tree condition on the associated Bergman tree . Combined with recent results about interpolating sequences this leads, for this range of s, to a characterization of universal interpolating sequences for and also for its multiplier algebra. However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury�Arveson Hardy Space . We show that µ is a Carleson measure for if and only if both the simple condition and the split tree condition hold. This gives a sharp estimate for Drury's generalization of von Neumann's operator inequality to the complex ball, and also provides a universal characterization of Carleson measures, up to dimensional constants, for Hilbert Spaces with a complete continuous Nevanlinna�Pick kernel function. We give a detailed analysis of the split tree condition for measures supported on embedded two manifolds and we find that in some generic cases the condition simplifies. We also establish a connection between function Spaces on embedded two manifolds and Hardy Spaces of plane domains
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carleson measures for the drury arveson Hardy Space and other besov sobolev Spaces on complex balls
arXiv: Complex Variables, 2007Co-Authors: Nicola Arcozzi, Richard Rochberg, Eric T SawyerAbstract:We characterize the Carleson measures for the Drury-Arveson Hardy Space and other Hilbert Spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy Space.
Brett D Wick - One of the best experts on this subject based on the ideXlab platform.
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weak factorizations of the Hardy Space h 1 mathbb r n in terms of multilinear riesz transforms
Canadian Mathematical Bulletin, 2017Co-Authors: Ji Li, Brett D WickAbstract:This paper provides a constructive proof of the weak factorization of the classical Hardy Space ${{H}^{1}}({{\mathbb{R}}^{n}})$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of $BMO({{\mathbb{R}}^{n}})$ (the dual of ${{H}^{1}}({{\mathbb{R}}^{n}})$ ) via commutators of the multilinear Riesz transforms.
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the corona theorem for the drury arveson Hardy Space and other holomorphic besov sobolev Spaces on the unit ball in c n
Analysis & PDE, 2011Co-Authors: şerban Costea, Eric T Sawyer, Brett D WickAbstract:We prove that the multiplier algebra of the Drury-Arveson Hardy Space H-n(2) on the unit ball in C-n has no corona in its maximal ideal Space, thus generalizing the corona theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach Space result: the Besov-Sobolev Space B-p(sigma) has the "baby corona property" for all sigma >= 0 and 1 < p < infinity. In addition we obtain infinite generator and semi-infinite matrix versions of these theorems.
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function Spaces related to the dirichlet Space
arXiv: Complex Variables, 2008Co-Authors: Nicola Arcozzi, Eric T Sawyer, Richard Rochberg, Brett D WickAbstract:We present results about Spaces of holomorphic functions associated to the classical Dirichlet Space. The Spaces we consider have roles similar to the roles of $H^{1}$ and $BMO$ in the Hardy Space theory and we emphasize those analogies.
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the corona theorem for the drury arveson Hardy Space and other holomorphic besov sobolev Spaces on the unit ball in mathbb c n
arXiv: Complex Variables, 2008Co-Authors: şerban Costea, Eric T Sawyer, Brett D WickAbstract:We prove that the multiplier algebra of the Drury-Arveson Hardy Space $H_{n}^{2}$ on the unit ball in $\mathbb{C}^{n}$ has no corona in its maximal ideal Space, thus generalizing the famous Corona Theorem of L. Carleson to higher dimensions. This result is obtained as a corollary of the Toeplitz corona theorem and a new Banach Space result: the Besov-Sobolev Space $B_{p}^{\sigma}$ has the "baby corona property" for all $\sigma \geq 0$ and $1
Ji Li - One of the best experts on this subject based on the ideXlab platform.
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weak factorizations of the Hardy Space h 1 mathbb r n in terms of multilinear riesz transforms
Canadian Mathematical Bulletin, 2017Co-Authors: Ji Li, Brett D WickAbstract:This paper provides a constructive proof of the weak factorization of the classical Hardy Space ${{H}^{1}}({{\mathbb{R}}^{n}})$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of $BMO({{\mathbb{R}}^{n}})$ (the dual of ${{H}^{1}}({{\mathbb{R}}^{n}})$ ) via commutators of the multilinear Riesz transforms.
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Hardy Space theory on Spaces of homogeneous type via orthonormal wavelet bases
Applied and Computational Harmonic Analysis, 2016Co-Authors: Ji Li, Lesley WardAbstract:Abstract In this paper, we first show that the remarkable orthonormal wavelet expansion for L p constructed recently by Auscher and Hytonen also converges in certain Spaces of test functions and distributions. Hence we establish the theory of product Hardy Spaces on Spaces X ˜ = X 1 × X 2 × ⋅ ⋅ ⋅ × X n , where each factor X i is a Space of homogeneous type in the sense of Coifman and Weiss. The main tool we develop is the Littlewood–Paley theory on X ˜ , which in turn is a consequence of a corresponding theory on each factor Space. We define the square function for this theory in terms of the wavelet coefficients. The Hardy Space theory developed in this paper includes product H p , the dual CMO p of H p with the special case BMO = CMO 1 , and the predual VMO of H 1 . We also use the wavelet expansion to establish the Calderon–Zygmund decomposition for product H p , and deduce an interpolation theorem. We make no additional assumptions on the quasi-metric or the doubling measure for each factor Space, and thus we extend to the full generality of product Spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving the Littlewood–Paley theory and function Spaces. Moreover, our methods would be expected to be a powerful tool for developing wavelet analysis on Spaces of homogeneous type.
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Hardy Space theory on Spaces of homogeneous type via orthonormal wavelet bases
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Ji Li, Lesley WardAbstract:In this paper, using the remarkable orthonormal wavelet basis constructed recently by Auscher and Hyt\"onen, we establish the theory of product Hardy Spaces on Spaces ${\widetilde X} = X_1\times X_2\times\cdot \cdot\cdot\times X_n$, where each factor $X_i$ is a Space of homogeneous type in the sense of Coifman and Weiss. The main tool we develop is the Littlewood--Paley theory on $\widetilde X$, which in turn is a consequence of a corresponding theory on each factor Space. We define the square function for this theory in terms of the wavelet coefficients. The Hardy Space theory developed in this paper includes product~$H^p$, the dual $\cmo^p$ of $H^p$ with the special case $\bmo = \cmo^1$, and the predual $\vmo$ of $H^1$. We also use the wavelet expansion to establish the Calder\'on--Zygmund decomposition for product $H^p$, and deduce an interpolation theorem. We make no additional assumptions on the quasi-metric or the doubling measure for each factor Space, and thus we extend to the full generality of product Spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving the Littlewood--Paley theory and function Spaces. Moreover, our methods would be expected to be a powerful tool for developing wavelet analysis on Spaces of homogeneous type.
Lesley Ward - One of the best experts on this subject based on the ideXlab platform.
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Hardy Space theory on Spaces of homogeneous type via orthonormal wavelet bases
Applied and Computational Harmonic Analysis, 2016Co-Authors: Ji Li, Lesley WardAbstract:Abstract In this paper, we first show that the remarkable orthonormal wavelet expansion for L p constructed recently by Auscher and Hytonen also converges in certain Spaces of test functions and distributions. Hence we establish the theory of product Hardy Spaces on Spaces X ˜ = X 1 × X 2 × ⋅ ⋅ ⋅ × X n , where each factor X i is a Space of homogeneous type in the sense of Coifman and Weiss. The main tool we develop is the Littlewood–Paley theory on X ˜ , which in turn is a consequence of a corresponding theory on each factor Space. We define the square function for this theory in terms of the wavelet coefficients. The Hardy Space theory developed in this paper includes product H p , the dual CMO p of H p with the special case BMO = CMO 1 , and the predual VMO of H 1 . We also use the wavelet expansion to establish the Calderon–Zygmund decomposition for product H p , and deduce an interpolation theorem. We make no additional assumptions on the quasi-metric or the doubling measure for each factor Space, and thus we extend to the full generality of product Spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving the Littlewood–Paley theory and function Spaces. Moreover, our methods would be expected to be a powerful tool for developing wavelet analysis on Spaces of homogeneous type.
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Hardy Space theory on Spaces of homogeneous type via orthonormal wavelet bases
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Ji Li, Lesley WardAbstract:In this paper, using the remarkable orthonormal wavelet basis constructed recently by Auscher and Hyt\"onen, we establish the theory of product Hardy Spaces on Spaces ${\widetilde X} = X_1\times X_2\times\cdot \cdot\cdot\times X_n$, where each factor $X_i$ is a Space of homogeneous type in the sense of Coifman and Weiss. The main tool we develop is the Littlewood--Paley theory on $\widetilde X$, which in turn is a consequence of a corresponding theory on each factor Space. We define the square function for this theory in terms of the wavelet coefficients. The Hardy Space theory developed in this paper includes product~$H^p$, the dual $\cmo^p$ of $H^p$ with the special case $\bmo = \cmo^1$, and the predual $\vmo$ of $H^1$. We also use the wavelet expansion to establish the Calder\'on--Zygmund decomposition for product $H^p$, and deduce an interpolation theorem. We make no additional assumptions on the quasi-metric or the doubling measure for each factor Space, and thus we extend to the full generality of product Spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving the Littlewood--Paley theory and function Spaces. Moreover, our methods would be expected to be a powerful tool for developing wavelet analysis on Spaces of homogeneous type.
Nicola Arcozzi - One of the best experts on this subject based on the ideXlab platform.
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invariant metrics for the quaternionic Hardy Space
arXiv: Complex Variables, 2013Co-Authors: Nicola Arcozzi, Giulia SarfattiAbstract:Riemannian metrics on the unit ball of the quaternions, which are naturally associated with the reproducing kernel Hilbert Spaces. We study the metric arising from the Hardy Space in detail. We show that, in contrast to the one-complex variable case, no Riemannian metric is invariant under regular self-maps of the quaternionic ball.
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function Spaces related to the dirichlet Space
arXiv: Complex Variables, 2008Co-Authors: Nicola Arcozzi, Eric T Sawyer, Richard Rochberg, Brett D WickAbstract:We present results about Spaces of holomorphic functions associated to the classical Dirichlet Space. The Spaces we consider have roles similar to the roles of $H^{1}$ and $BMO$ in the Hardy Space theory and we emphasize those analogies.
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carleson measures for the drury arveson Hardy Space and other besov sobolev Spaces on complex balls
Advances in Mathematics, 2008Co-Authors: Nicola Arcozzi, Richard Rochberg, Eric T SawyerAbstract:For 0s<1/2 we characterize Carleson measures µ for the analytic Besov�Sobolev Spaces on the unit ball in by the discrete tree condition on the associated Bergman tree . Combined with recent results about interpolating sequences this leads, for this range of s, to a characterization of universal interpolating sequences for and also for its multiplier algebra. However, the tree condition is not necessary for a measure to be a Carleson measure for the Drury�Arveson Hardy Space . We show that µ is a Carleson measure for if and only if both the simple condition and the split tree condition hold. This gives a sharp estimate for Drury's generalization of von Neumann's operator inequality to the complex ball, and also provides a universal characterization of Carleson measures, up to dimensional constants, for Hilbert Spaces with a complete continuous Nevanlinna�Pick kernel function. We give a detailed analysis of the split tree condition for measures supported on embedded two manifolds and we find that in some generic cases the condition simplifies. We also establish a connection between function Spaces on embedded two manifolds and Hardy Spaces of plane domains
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carleson measures for the drury arveson Hardy Space and other besov sobolev Spaces on complex balls
arXiv: Complex Variables, 2007Co-Authors: Nicola Arcozzi, Richard Rochberg, Eric T SawyerAbstract:We characterize the Carleson measures for the Drury-Arveson Hardy Space and other Hilbert Spaces of analytic functions of several complex variables. This provides sharp estimates for Drury's generalization of Von Neumann's inequality. The characterization is in terms of a geometric condition, the "split tree condition", which reflects the nonisotropic geometry underlying the Drury-Arveson Hardy Space.
