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Sundaram Thangavelu - One of the best experts on this subject based on the ideXlab platform.
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on the maximal function associated to the spherical means on the Heisenberg Group
arXiv: Classical Analysis and ODEs, 2018Co-Authors: S Bagchi, S Hait, L Roncal, Sundaram ThangaveluAbstract:In this paper we deal with lacunary and full versions of the spherical maximal function on the Heisenberg Group. We first investigate the $L^p$ boundedness of the lacunary maximal function associated to the spherical means on the Heisenberg Group. By suitable adaptation of an approach of M. Lacey in the Euclidean case, we obtain sparse bounds for these maximal functions, which lead to new unweighted and weighted estimates. In order to prove the result, several properties of the spherical means have to be accomplished, namely, the $L^p$ improving property of the operator and a continuity property. With the help of the results just proved for the lacunary spherical means, we also obtain new $L^p-L^q$ estimates for the local version of the full maximal function, that in turn is used to get sparse domination for the full maximal function.
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Weighted norm inequalities for Weyl multipliers and fourier multipliers on the Heisenberg Group
Journal D Analyse Mathematique, 2018Co-Authors: Sayan Bagchi, Sundaram ThangaveluAbstract:In this paper, we prove weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg Group and also show, in the context of a theorem of Weis on operator-valued Fourier multipliers, that R-boundedness of the derivative of the multiplier is not necessary for boundedness of the multiplier transform.
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Weighted norm inequalities for Weyl multipliers and Fourier multipliers on the Heisenberg Group
arXiv: Functional Analysis, 2013Co-Authors: Sayan Bagchi, Sundaram ThangaveluAbstract:In this paper we prove weighted norm inequalities for Weyl multipliers satisfying Mauceri's condition. As applications of this we obtain some estimates for $L^p$ multipliers on the Heisenberg Group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform.
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harmonic analysis on the Heisenberg Group
2012Co-Authors: Sundaram ThangaveluAbstract:The Group Fourier transform analysis of the sublaplacian Group algebras and applications the reduced Heisenberg Group.
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the heat kernel transform for the Heisenberg Group
Journal of Functional Analysis, 2005Co-Authors: Bernhard Krotz, Sundaram ThangaveluAbstract:Abstract The heat kernel transform H t is studied for the Heisenberg Group in detail. The main result shows that the image of H t is a direct sum of two weighted Bergman spaces, in contrast to the classical case of R n and compact symmetric spaces, and the weight functions are found to be (surprisingly) not non-negative.
Séverine Rigot - One of the best experts on this subject based on the ideXlab platform.
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The Besicovitch covering property in the Heisenberg Group revisited
The Journal of Geometric Analysis, 2018Co-Authors: Sebastiano Golo, Séverine RigotAbstract:The Besicovitch covering property (BCP) is known to be one of the fundamental tools in measure theory, and more generally, a useful property for numerous purposes in analysis and geometry. We prove both sufficient and necessary criteria for the validity of BCP in the first Heisenberg Group equipped with a homogeneous distance. Beyond recovering all previously known results about the validity or non-validity of BCP in this setting, we get simple descriptions of new large classes of homogeneous distances satisfying BCP. We also obtain a full characterization of rotationally invariant distances for which BCP holds in the first Heisenberg Group under mild regularity assumptions about their unit sphere.
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optimal mass transportation in the Heisenberg Group
Journal of Functional Analysis, 2004Co-Authors: Luigi Ambrosio, Séverine RigotAbstract:In this paper we consider the problem of optimal transportation of absolutely continuous masses in the Heisenberg Group Hn, in the case when the cost function is either the square of the Carnot–Caratheodory distance or the square of the Koranyi norm. In both cases we show existence and uniqueness of an optimal transport map. In the former case the proof requires a delicate analysis of minimizing geodesics of the Group and of the differentiability properties of the squared distance function. In the latter case the proof requires some fine properties of BV functions in the Heisenberg Group.
Essin Turhan - One of the best experts on this subject based on the ideXlab platform.
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frenet equations of spacelike biharmonic curves with timelike binormal in terms of exponential maps according to flat metric in lorentzian Heisenberg Group heis 3
2013Co-Authors: Talat Körpinar, Essin TurhanAbstract:In this paper, we study Frenet representations of spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg Group Heis 3 . We characterize spacelike biharmonic curves with timelike binormal in terms of exponential maps in the Lorentzian Heisenberg Group Heis 3 .
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a new approach on smarandache tn1 curves in terms of spacelike biharmonic curves with a timelike binormal in the lorentzian Heisenberg Group heis
viXra, 2011Co-Authors: Talat Körpinar, Essin TurhanAbstract:2 ABSTRACT : In this paper, we study spacelike biharmonic curve with a timelike binormal in the Lorentzian Heisenberg Group Heis 3 . We define a special case of such curves and call it Smarandache 1 tn curves in the Lorentzian Heisenberg Group Heis 3 . We construct parametric equations of Smarandache 1 tn curves in terms of spacelike biharmonic curves with a timelike binormal in the Lorentzian Heisenberg Group Heis 3 .
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on characterization of timelike horizontal biharmonic curves in the lorentzian Heisenberg Group heis3
Zeitschrift für Naturforschung A, 2010Co-Authors: Essin Turhan, Talat KörpinarAbstract:In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg Group Heis 3 . We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves.
Talat Körpinar - One of the best experts on this subject based on the ideXlab platform.
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frenet equations of spacelike biharmonic curves with timelike binormal in terms of exponential maps according to flat metric in lorentzian Heisenberg Group heis 3
2013Co-Authors: Talat Körpinar, Essin TurhanAbstract:In this paper, we study Frenet representations of spacelike biharmonic curves with timelike binormal according to flat metric in the Lorentzian Heisenberg Group Heis 3 . We characterize spacelike biharmonic curves with timelike binormal in terms of exponential maps in the Lorentzian Heisenberg Group Heis 3 .
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a new approach on smarandache tn1 curves in terms of spacelike biharmonic curves with a timelike binormal in the lorentzian Heisenberg Group heis
viXra, 2011Co-Authors: Talat Körpinar, Essin TurhanAbstract:2 ABSTRACT : In this paper, we study spacelike biharmonic curve with a timelike binormal in the Lorentzian Heisenberg Group Heis 3 . We define a special case of such curves and call it Smarandache 1 tn curves in the Lorentzian Heisenberg Group Heis 3 . We construct parametric equations of Smarandache 1 tn curves in terms of spacelike biharmonic curves with a timelike binormal in the Lorentzian Heisenberg Group Heis 3 .
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on characterization of timelike horizontal biharmonic curves in the lorentzian Heisenberg Group heis3
Zeitschrift für Naturforschung A, 2010Co-Authors: Essin Turhan, Talat KörpinarAbstract:In this paper, we study energy of time-like horizontal biharmonic curves in the Lorentzian Heisenberg Group Heis 3 . We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of the biharmonic curves are helices. Finally, we study the mechanics of biharmonic curves and provide conditions for energy of horizontal biharmonic curves.
Azita Mayeli - One of the best experts on this subject based on the ideXlab platform.
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a density condition for interpolation on the Heisenberg Group
Rocky Mountain Journal of Mathematics, 2012Co-Authors: Bradley Currey, Azita MayeliAbstract:(N). We prove a necessary and sufficient density conditionin order that such subsspaces possess the interpolation property with respect toa class of discrete subsets of N that includes the integer lattice. We exhibit aconcrete example of a subspace that has interpolation for the integer lattice, andwe also prove a necessary and sufficient condition for shift invariant subspaces topossess a singly-generated orthonormal basis of translates.Mathematics Subject Classification (2000): 42C15, 92A20, 43A80.Keywords and phrases: The Heisenberg Group, Heisenberg frame, Gabor frame, multiplicity freesubspaces, sampling spaces, the interpolation property
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a density condition for interpolation on the Heisenberg Group
arXiv: Representation Theory, 2010Co-Authors: Bradley Currey, Azita MayeliAbstract:Let $N$ be the Heisenberg Group. We consider left-invariant multiplicity free subspaces of $L^2(N)$. We prove a necessary and sufficient density condition in order that such subspaces possess the interpolation property with respect to a class of discrete subsets of $N$ that includes the integer lattice. We exhibit a concrete example of a subspace that has interpolation for the integer lattice, and we also prove a necessary and sufficient condition for shift invariant subspaces to possess a singly-generated orthonormal basis of translates.