Riesz potential and its commutators on generalized weighted Orlicz–Morrey spaces

Guliyev, Vagif S.; Deringoz, Fatih

doi:10.1002/mana.201900559

Cited by 4 publications

(2 citation statements)

References 43 publications

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“…(i) Let all the symbols be the same as in Theorem 4.3. By[76, Lemma 7.2], Remark 3.2, and the definition ofH M p r (R n ), we find that, if r ∈ (1, ∞), then H M p r (R n ) = M p r (R n ).In this case, Theorem 4.3 coincides with [1, Theorem 3.1] (see also[25, Corollary 4.7]). Moreover, to the best of our knowledge, Theorem 4.3 is new even when r ∈ (0, 1].…”

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confidence: 58%

“…Indeed, the known proof of fractional integrals on concrete spaces (see, for instance, [25]) is strongly based on the various indexes of concrete spaces, and is inapplicable for the Hardy space H X (R n ) here due to the deficiency of the explicit expression of the (quasi-)norm of X. We use two methods to overcome this essential difficulty.…”

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

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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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confidence: 58%

Section: Introductionmentioning

confidence: 99%