Fractional integral operators on Orlicz slice Hardy spaces

Ho, Kwok Pun Victor

doi:10.1007/s13540-022-00043-1

Cited by 22 publications

(7 citation statements)

References 20 publications

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“…Remark 2. 13 Note that the Orlicz-Lorentz-Karamata space just defined is slightly different from the definition in [24,25]. However, taking some mild restrictions on , we find that these definitions are equivalent.…”

Section: Orlicz-lorentz-karamata Spacesmentioning

confidence: 88%

“…In 2017, Liu and Zhou [37] investigated the boundedness of fractional integral operators on Lorentz-Karamata martingale spaces. Motivated by these results, the authors [25,26] introduced a class of Orlicz-Lorentz-Karamata spaces, which are much wider than the Lorentz-Karamata spaces or the Orlicz-Lorentz spaces and other important function spaces, and then developed a theory of the martingale Hardy spaces in the new framework. The method of atomic decomposition as one of results about martingale Hardy Orlicz-Lorentz-Karamata spaces comes from [33], which is a very useful tool in martingale theory.…”

Section: Introductionmentioning

confidence: 99%

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Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

Hao,

Li,

Weisz

2024

Banach J. Math. Anal.

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In this article, we discuss the applications of martingale Hardy Orlicz–Lorentz–Karamata spaces in Fourier analysis. More precisely, we show that the partial sums of the Walsh–Fourier series converge to the function in norm if $$f\in L_{\Phi ,q,b}$$ f ∈ L Φ , q , b with $$1<p_-\le p_+<\infty $$ 1 < p - ≤ p + < ∞ . The equivalence of maximal operators on martingale Hardy Orlicz–Lorentz–Karamata spaces is presented. The Fejér summability method is also studied and it is proved that the maximal Fejér operator is bounded from martingale Hardy Orlicz–Lorentz–Karamata spaces to Orlicz–Lorentz–Karamata spaces. As a consequence, we obtain conclusions about almost everywhere and norm convergence of Fejér means.

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Section: Orlicz-lorentz-karamata Spacesmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

Hao,

Li,

Weisz

2024

Banach J. Math. Anal.

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“…(ii) The extrapolation theorem on weighted Lebesgue spaces was originally established by Rubio de Francia in [54] and has been widely used in the study of sublinear operators on Hardy-type spaces. We refer the reader to [10,29,31] for more studies on this.…”

Section: Preliminariesmentioning

confidence: 99%

Boundedness of Fractional Integrals on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Chen¹,

Jia²,

Yang³

2022

Preprint

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Let X be a ball quasi-Banach function space on R n and H X (R n ) the Hardy space associated with X, and let α ∈ (0, n) and β ∈ (1, ∞). In this article, assuming that the (powered) Hardy-Littlewood maximal operator satisfies the Fefferman-Stein vector-valued maximal inequality on X and is bounded on the associate space of X, the authors prove that the fractional integral I α can be extended to a bounded linear operator fromand only if there exists a positive constant C such that, for any ballX , where X β denotes the β-convexification of X. Moreover, under some different reasonable assumptions on both X and another ball quasi-Banach function space Y, the authors also consider the mapping property of I α from H X (R n ) to H Y (R n ) via using the extrapolation theorem. All these results have a wide range of applications. Particularly, when these are applied, respectively, to Morrey spaces, mixed-norm Lebesgue spaces, local generalized Herz spaces, and mixed-norm Herz spaces, all these results are new. The proofs of these theorems strongly depend on atomic and molecular characterizations of H X (R n ).

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“…The Orlicz space was introduced to cover the failure of the boundedness of some integral operators. We refer the reader to [2,28,34,53] for more studies on this.…”

Section: Orlicz Spacesmentioning

confidence: 99%

Boundedness of Calderón–Zygmund operators on ball Campanato-type function spaces

2022

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Let X be a ball quasi-Banach function space on R n satisfying some mild assumptions. In this article, the authors first find a reasonable version T of the Calderón-Zygmund operator T on the ball Campanato-type function space L X,q,s,d (R n ) with q ∈ [1, ∞), s ∈ Z n + , and d ∈ (0, ∞). Then the authors prove that T is bounded on L X,q,s,d (R n ) if and only if, for any γ ∈ Z n + with |γ| ≤ s, T * (x γ ) = 0, which is hence sharp. Moreover, T is proved to be the adjoint operator of T , which further strengthens the rationality of the definition of T . All these results have a wide range of applications. In particular, even when they are applied, respectively, to weighted Lebesgue spaces, variable Lebesgue spaces, Orlicz spaces, Orliczslice spaces, Morrey spaces, mixed-norm Lebesgue spaces, local generalized Herz spaces, and mixed-norm Herz spaces, all the obtained results are new. The proofs of these results strongly depend on the properties of the kernel of T under consideration and also on the dual theorem on L X,q,s,d (R n ).

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Fractional integral operators on Orlicz slice Hardy spaces

Cited by 22 publications

References 20 publications

Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

Applications of martingale Hardy Orlicz–Lorentz–Karamata theory in Fourier analysis

Boundedness of Fractional Integrals on Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Boundedness of Calderón–Zygmund operators on ball Campanato-type function spaces

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