Fourier transform of anisotropic mixed-norm Hardy spaces

Huang, Long; Chang, Der–Chen; Yang, Dachun

doi:10.1007/s11464-021-0906-9

Cited by 23 publications

(14 citation statements)

References 30 publications

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“…whose associated basic function space is the variable Lebesgue space L p(•) (R n ); Obviously, L p (R n ) and L p(•) (R n ) cannot cover each other, so do [17,Theorem 2.4] and Theorem 3.1 of the present article.…”

Section: Coincides With the Anisotropic Hardy Spacementioning

confidence: 88%

“…. , p n ) ∈ (0, 1] n are two vectors; see [18,17]. On another hand, as a generalization of the classical Hardy space H p (R n ), the variable Hardy space H p(•) (R n ), in which the constant exponent p is replaced by a variable exponent function p(•) : R n → (0, ∞], was first studied by Nakai and Sawano [23] and, independently, by Cruz-Uribe and Wang [11] with some weaker assumptions on p(•) than those used in [23].…”

Section: Introductionmentioning

confidence: 99%

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Fourier Transform of Variable Anisotropic Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Li¹

2021

Preprint

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Let p(•) : R n → (0, 1] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on R n . Let H p(•) A (R n ) be the variable anisotropic Hardy space associated with A defined via the radial maximal function. In this article, via the known atomic characterization of H p(•)A (R n ) and establishing two useful estimates on anisotropic variable atoms, the author shows that the Fourier transform f of f ∈ H p (•) A (R n ) coincides with a continuous function F in the sense of tempered distributions, and F satisfies a pointwise inequality which contains a step function with respect to A as well as the Hardy space norm of f . As applications, the author also obtains a higher order convergence of the continuous function F at the origin. Finally, an analogue of the Hardy-Littlewood inequality in the variable anisotropic Hardy space setting is also presented. All these results are new even in the classical isotropic setting.

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Section: Coincides With the Anisotropic Hardy Spacementioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Fourier Transform of Variable Anisotropic Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Li¹

2021

Preprint

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“…[5] on mixed-norm Morrey spaces, in refs. [1,[6][7][8][9][10][11][12] on mixed-norm Hardy spaces, as well as in [13][14][15][16][17] on mixed-norm Besov spaces and mixed-norm Triebel-Lizorkin spaces. For more details on the progress made with regard to the theory of mixed-norm function spaces, we refer the reader to [18][19][20][21][22][23][24][25][26][27] as well as to the survey article [28].…”

Section: Introductionmentioning

confidence: 99%

Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

2021

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Let p→∈(0,∞)n be an exponent vector and A be a general expansive matrix on Rn. Let HAp→(Rn) be the anisotropic mixed-norm Hardy spaces associated with A defined via the non-tangential grand maximal function. In this article, using the known atomic characterization of HAp→(Rn), the authors characterize this Hardy space via molecules with the best possible known decay. As an application, the authors establish a criterion on the boundedness of linear operators from HAp→(Rn) to itself, which is used to explore the boundedness of anisotropic Calderón–Zygmund operators on HAp→(Rn). In addition, the boundedness of anisotropic Calderón–Zygmund operators from HAp→(Rn) to the mixed-norm Lebesgue space Lp→(Rn) is also presented. The obtained boundedness of these operators positively answers a question mentioned by Cleanthous et al. All of these results are new, even for isotropic mixed-norm Hardy spaces on Rn.

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“…. , p n ) ∈ (0, 1] n ; see, respectively, [15,16]. In addition, motivated by the previous work of [8,12,17], Huang et al [18] introduced the anisotropic mixed-norm Hardy space H p A (R n ) with respect to p ∈ (0, ∞) n and a dilation A, and investigated its various real-variable characterizations.…”

Section: Introductionmentioning

confidence: 99%

Fourier Transform of Anisotropic Mixed-norm Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Li¹,

Lu²,

Zhang³

2021

Preprint

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Let p ∈ (0, 1] n be a n-dimensional vector and A a dilation. Let H p A (R n ) denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of H p A (R n ) and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of f ∈ H p A (R n ) coincides with a continuous function F on R n in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of H p A (R n ).

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Fourier transform of anisotropic mixed-norm Hardy spaces

Cited by 23 publications

References 30 publications

Fourier Transform of Variable Anisotropic Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Fourier Transform of Variable Anisotropic Hardy Spaces with Applications to Hardy-Littlewood Inequalities

Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

Fourier Transform of Anisotropic Mixed-norm Hardy Spaces with Applications to Hardy-Littlewood Inequalities

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