The Experts below are selected from a list of 28440 Experts worldwide ranked by ideXlab platform
Ian Tice - One of the best experts on this subject based on the ideXlab platform.
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Lorentz Space ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY
Communications in Contemporary Mathematics, 2012Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier–Serfaty [From the Ginzburg–Landau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz Space estimates for the Ginzburg–Landau energy, J. Funct. Anal. 254(3) (2008) 773–825], which couples the "ball construction method" to estimates in the Lorentz Space L2,∞.
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Lorentz Space estimates for the coulombian renormalized energy
arXiv: Analysis of PDEs, 2011Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier-Serfaty \cite{ss1,ss3}. To derive the estimates, we use a technique that we introduced in \cite{st}, which couples the "ball construction method" to estimates in the Lorentz Space $L^{2,\infty}$.
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Lorentz Space estimates for the Ginzburg–Landau energy
Journal of Functional Analysis, 2008Co-Authors: Sylvia Serfaty, Ian TiceAbstract:Abstract In this paper we prove novel lower bounds for the Ginzburg–Landau energy with or without magnetic field. These bounds rely on an improvement of the “vortex-balls construction” estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz Space norm, on which it thus provides an upper bound. The Lorentz Space L 2 , ∞ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.
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Lorentz Space Estimates for the Ginzburg-Landau Energy
arXiv: Analysis of PDEs, 2007Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz Space norm, on which it thus provides an upper bound. The Lorentz Space $L^{2,\infty}$ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.
Sylvia Serfaty - One of the best experts on this subject based on the ideXlab platform.
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Lorentz Space ESTIMATES FOR THE COULOMBIAN RENORMALIZED ENERGY
Communications in Contemporary Mathematics, 2012Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier–Serfaty [From the Ginzburg–Landau model to vortex lattice problems, to appear in Comm. Math. Phys. (2012); One-dimensional log gases and the renormalized energy, in preparation]. To derive the estimates, we use a technique that we introduced in [Lorentz Space estimates for the Ginzburg–Landau energy, J. Funct. Anal. 254(3) (2008) 773–825], which couples the "ball construction method" to estimates in the Lorentz Space L2,∞.
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Lorentz Space estimates for the coulombian renormalized energy
arXiv: Analysis of PDEs, 2011Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier-Serfaty \cite{ss1,ss3}. To derive the estimates, we use a technique that we introduced in \cite{st}, which couples the "ball construction method" to estimates in the Lorentz Space $L^{2,\infty}$.
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Lorentz Space estimates for the Ginzburg–Landau energy
Journal of Functional Analysis, 2008Co-Authors: Sylvia Serfaty, Ian TiceAbstract:Abstract In this paper we prove novel lower bounds for the Ginzburg–Landau energy with or without magnetic field. These bounds rely on an improvement of the “vortex-balls construction” estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz Space norm, on which it thus provides an upper bound. The Lorentz Space L 2 , ∞ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.
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Lorentz Space Estimates for the Ginzburg-Landau Energy
arXiv: Analysis of PDEs, 2007Co-Authors: Sylvia Serfaty, Ian TiceAbstract:In this paper we prove novel lower bounds for the Ginzburg-Landau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz Space norm, on which it thus provides an upper bound. The Lorentz Space $L^{2,\infty}$ we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results.
Wen Yuan - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation
arXiv: Classical Analysis and ODEs, 2017Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-Holder continuous condition, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz Space $H_A^{p(\cdot),q}(\mathbb R^n)$ associated with $A$, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of $H_A^{p(\cdot),q}(\mathbb R^n)$, respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy-Lorentz Space $H_A^{p(\cdot),q}(\mathbb R^n)$ severs as the intermediate Space between the anisotropic variable Hardy Space $H_A^{p(\cdot)}(\mathbb R^n)$ and the Space $L^\infty(\mathbb R^n)$ via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybiral on the variable Lorentz Space, further implies the coincidence between $H_A^{p(\cdot),q}(\mathbb R^n)$ and the variable Lorentz Space $L^{p(\cdot),q}(\mathbb R^n)$ when $\mathop\mathrm{essinf}_{x\in\mathbb{R}^n}p(x)\in (1,\infty)$.
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Anisotropic variable Hardy–Lorentz Spaces and their real interpolation
Journal of Mathematical Analysis and Applications, 2017Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Abstract Let p ( ⋅ ) : R n → ( 0 , ∞ ] be a variable exponent function satisfying the globally log-Holder continuous condition, q ∈ ( 0 , ∞ ] and A be a general expansive matrix on R n . In this article, the authors first introduce the anisotropic variable Hardy–Lorentz Space H A p ( ⋅ ) , q ( R n ) associated with A, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of H A p ( ⋅ ) , q ( R n ) , respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy–Lorentz Space H A p ( ⋅ ) , q ( R n ) serves as the intermediate Space between the anisotropic variable Hardy Space H A p ( ⋅ ) ( R n ) and the Space L ∞ ( R n ) via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybiral on the variable Lorentz Space, further implies the coincidence between H A p ( ⋅ ) , q ( R n ) and the variable Lorentz Space L p ( ⋅ ) , q ( R n ) when ess inf x ∈ R n p ( x ) ∈ ( 1 , ∞ ) .
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Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. Let $H^{p,q}_A(\mathbb{R}^n)$ be the anisotropic Hardy-Lorentz Spaces associated with $A$ defined via the non-tangential grand maximal function. In this article, the authors characterize $H^{p,q}_A(\mathbb{R}^n)$ in terms of the Lusin-area function, the Littlewood-Paley $g$-function or the Littlewood-Paley $g_\lambda^*$-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz Space $L^{p,q}(\mathbb{R}^n)$. All these characterizations are new even for the classical isotropic Hardy-Lorentz Spaces on $\mathbb{R}^n$. Moreover, the range of $\lambda$ in the $g_\lambda^*$-function characterization of $H^{p,q}_A(\mathbb{R}^n)$ coincides with the best known one in the classical Hardy Space $H^p(\mathbb{R}^n)$ or in the anisotropic Hardy Space $H^p_A(\mathbb{R}^n)$.
Sergey V. Astashkin - One of the best experts on this subject based on the ideXlab platform.
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Compact and strictly singular operators in rearrangement invariant Spaces and Rademacher functions
Positivity, 2020Co-Authors: Sergey V. AstashkinAbstract:We refine some earlier results by Flores, Hernandez, Semenov, and Tradacete on compactness of the square of strictly singular endomorphisms and identifying general Banach lattices with the Kato property in the setting of rearrangement invariant Spaces on [0, 1]. A Banach Space X is said to have the Kato property if every strictly singular operator acting in X is compact. We show that each strictly singular operator bounded in a disjointly homogeneous rearrangement invariant Space with the non-trivial Boyd indices has compact square, and that the Kato property is shared by a 2-disjointly homogeneous rearrangement invariant Space X whenever $$X\supset G$$, where G is the closure of $$L_\infty $$ in the Orlicz Space, generated by the function $$e^{u^2}-1$$. Moreover, a partial converse to the latter result is given under the assumption that $$X\subset L\log ^{1/2}L$$. As an application we find rather sharp conditions, under which a Lorentz Space $$\Lambda (2,\psi )$$ possesses the Kato property. In particular, $$\Lambda (2,\log ^{-\alpha }(e/u))$$, with $$0
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Compact and strictly singular operators in rearrangement invariant Spaces and Rademacher functions
Positivity, 2020Co-Authors: Sergey V. AstashkinAbstract:We refine some earlier results by Flores, Hernández, Semenov, and Tradacete on compactness of the square of strictly singular endomorphisms and identifying general Banach lattices with the Kato property in the setting of rearrangement invariant Spaces on [0, 1]. A Banach Space X is said to have the Kato property if every strictly singular operator acting in X is compact. We show that each strictly singular operator bounded in a disjointly homogeneous rearrangement invariant Space with the non-trivial Boyd indices has compact square, and that the Kato property is shared by a 2-disjointly homogeneous rearrangement invariant Space X whenever $$X\supset G$$ X ⊃ G , where G is the closure of $$L_\infty $$ L ∞ in the Orlicz Space, generated by the function $$e^{u^2}-1$$ e u 2 - 1 . Moreover, a partial converse to the latter result is given under the assumption that $$X\subset L\log ^{1/2}L$$ X ⊂ L log 1 / 2 L . As an application we find rather sharp conditions, under which a Lorentz Space $$\Lambda (2,\psi )$$ Λ ( 2 , ψ ) possesses the Kato property. In particular, $$\Lambda (2,\log ^{-\alpha }(e/u))$$ Λ ( 2 , log - α ( e / u ) ) , with $$0
Jun Liu - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation
arXiv: Classical Analysis and ODEs, 2017Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-Holder continuous condition, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, the authors first introduce the anisotropic variable Hardy-Lorentz Space $H_A^{p(\cdot),q}(\mathbb R^n)$ associated with $A$, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of $H_A^{p(\cdot),q}(\mathbb R^n)$, respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy-Lorentz Space $H_A^{p(\cdot),q}(\mathbb R^n)$ severs as the intermediate Space between the anisotropic variable Hardy Space $H_A^{p(\cdot)}(\mathbb R^n)$ and the Space $L^\infty(\mathbb R^n)$ via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybiral on the variable Lorentz Space, further implies the coincidence between $H_A^{p(\cdot),q}(\mathbb R^n)$ and the variable Lorentz Space $L^{p(\cdot),q}(\mathbb R^n)$ when $\mathop\mathrm{essinf}_{x\in\mathbb{R}^n}p(x)\in (1,\infty)$.
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Anisotropic variable Hardy–Lorentz Spaces and their real interpolation
Journal of Mathematical Analysis and Applications, 2017Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Abstract Let p ( ⋅ ) : R n → ( 0 , ∞ ] be a variable exponent function satisfying the globally log-Holder continuous condition, q ∈ ( 0 , ∞ ] and A be a general expansive matrix on R n . In this article, the authors first introduce the anisotropic variable Hardy–Lorentz Space H A p ( ⋅ ) , q ( R n ) associated with A, via the radial grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain characterizations of H A p ( ⋅ ) , q ( R n ) , respectively, in terms of the atom and the Lusin area function. As an application, the authors prove that the anisotropic variable Hardy–Lorentz Space H A p ( ⋅ ) , q ( R n ) serves as the intermediate Space between the anisotropic variable Hardy Space H A p ( ⋅ ) ( R n ) and the Space L ∞ ( R n ) via the real interpolation. This, together with a special case of the real interpolation theorem of H. Kempka and J. Vybiral on the variable Lorentz Space, further implies the coincidence between H A p ( ⋅ ) , q ( R n ) and the variable Lorentz Space L p ( ⋅ ) , q ( R n ) when ess inf x ∈ R n p ( x ) ∈ ( 1 , ∞ ) .
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Littlewood-Paley Characterizations of Anisotropic Hardy-Lorentz Spaces
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Jun Liu, Dachun Yang, Wen YuanAbstract:Let $p\in(0,1]$, $q\in(0,\infty]$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. Let $H^{p,q}_A(\mathbb{R}^n)$ be the anisotropic Hardy-Lorentz Spaces associated with $A$ defined via the non-tangential grand maximal function. In this article, the authors characterize $H^{p,q}_A(\mathbb{R}^n)$ in terms of the Lusin-area function, the Littlewood-Paley $g$-function or the Littlewood-Paley $g_\lambda^*$-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz Space $L^{p,q}(\mathbb{R}^n)$. All these characterizations are new even for the classical isotropic Hardy-Lorentz Spaces on $\mathbb{R}^n$. Moreover, the range of $\lambda$ in the $g_\lambda^*$-function characterization of $H^{p,q}_A(\mathbb{R}^n)$ coincides with the best known one in the classical Hardy Space $H^p(\mathbb{R}^n)$ or in the anisotropic Hardy Space $H^p_A(\mathbb{R}^n)$.
