Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

Lu, Shanzhen; Yang, Dachun

doi:10.1002/mana.19981910112

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…Using a certain inhomogeneous Herz space, Sawano et al [88] ingeniously overcame the difficulty appearing in the proof of the convergence of the atomic decomposition of H X (R n ). For more progress on Herz spaces, we refer the reader to [61,71,42,75,60,117] for classical Herz spaces, to [85,97,118] for variable Herz spaces, and also to [46,47,78,58,66,67,68,72] for more applications of Herz spaces.…”

Section: Introductionmentioning

confidence: 99%

Mixed-Norm Herz Spaces and Their Applications in Related Hardy Spaces

Zhao¹,

Yang²,

Zhang³

2022

Preprint

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In this article, the authors introduce a class of mixed-norm Herz spaces, Ė α, p q (R n ), which is a natural generalization of mixed Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz-Thorin interpolation theorem on Ė α, p q (R n ). Applying these Riesz-Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy-Littlewood maximal operator and the Fefferman-Stein vector-valued maximal inequality on Ė α, p q (R n ). As applications, the authors develop various real-variable theory of Hardy spaces associated with Ė α, p q (R n ) by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of Ė α, p q (R n ) and the non-trivial constructions of auxiliary functions in the Riesz-Thorin interpolation theorem.

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Section: Introductionmentioning

confidence: 99%

Mixed-Norm Herz Spaces and Their Applications in Related Hardy Spaces

Zhao¹,

Yang²,

Zhang³

2022

Preprint

Self Cite

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Yang

1998

Acta Mathematica Hungarica

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Mixed-norm Herz spaces and their applications in related Hardy spaces

2022

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In this paper, the authors introduce a class of mixed-norm Herz spaces, [Formula: see text], which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on [Formula: see text]. Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on [Formula: see text]. As applications, the authors develop various real-variable theory of Hardy spaces associated with [Formula: see text] by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of [Formula: see text] and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem.

show abstract

Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

Cited by 3 publications

References 17 publications

Mixed-Norm Herz Spaces and Their Applications in Related Hardy Spaces

Mixed-Norm Herz Spaces and Their Applications in Related Hardy Spaces

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Mixed-norm Herz spaces and their applications in related Hardy spaces

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