Boundedness of Fractional Integral Operators on Hardy-Amalgam Spaces

Cheung, Ka Luen; Ho, Kwok Pun Victor; Yee, Tat Leung

doi:10.1155/2021/1142942

Cited by 6 publications

(4 citation statements)

References 27 publications

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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%

“…Moreover, let the Hardy-amalgam space (H p , l q )(R n ) := H (L p ,l q )(R n ) (R n ) be as in Definition 2.7 with X := (L p , l q )(R n ). Then Theorem 3.20 with both X := (L p , l q )(R n ) and Y := (L r , l s )(R n ) is a generalization of [10,Theorem 7], where r, s ∈ (0, ∞) are such that 1…”

Section: Preliminariesmentioning

confidence: 99%

“…Meanwhile, Huy and Ky [37] obtained the boundedness of fractional integrals on Musielak-Orlicz Hardy spaces. We refer the reader to [3,9,10,20,28,48,65] for more studies on the boundedness of fractional integrals on Hardy-type spaces.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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

Chen¹,

Jia²,

Yang³

2022

Preprint

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“…It is well known that the real-variable theory, including the boundedness of fractional integrals on Hardy-type spaces, plays a fundamental role in harmonic analysis and partial differential equations (see, for instance, [4,12,29,45,57,58]). Moreover, in recent years, the boundedness of fractional integrals on Campanato-type spaces has attracted more and more attention.…”

Section: Introductionmentioning

confidence: 99%

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Chen¹,

Jia²,

Yang³

2022

Preprint

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Let X be a ball quasi-Banach function space on R n satisfying some mild assumptions and let α ∈ (0, n) and β ∈ (1, ∞). In this article, when α ∈ (0, 1), the authors first find a reasonable version I α of the fractional integral I α 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 thatX , where X β denotes the β-convexification of X. Furthermore, the authors extend the range α ∈ (0, 1) in I α to the range α ∈ (0, n) and also obtain the corresponding boundedness in this case. Moreover, I α is proved to be the adjoint operator of I α . All these results have a wide range of applications. Particularly, even when they are applied, respectively, to 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 dual theorem on L X,q,s,d (R n ) and also on the special atomic decomposition of molecules of H X (R n ) (the Hardy-type space associated with X) which proves the predual space of L X,q,s,d (R n ).

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Fractional integral operators on Orlicz slice Hardy spaces

2022

Fract Calc Appl Anal

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Boundedness of Fractional Integral Operators on Hardy-Amalgam Spaces

Abstract: We establish the boundedness of the fractional integral operators on the Hardy-amalgam spaces.

Cited by 6 publications

References 27 publications

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

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

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Fractional integral operators on Orlicz slice Hardy spaces

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