Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

Wei, Mingquan; Sun, Lanyin

doi:10.1155/2022/4924127

Cited by 3 publications

(2 citation statements)

References 30 publications

(33 reference statements)

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“…, where 1 p + 1 p ′ = 1. We now claim that [69, Theorem 1] in the case when α ∈ (0, 1) ∩ (0, n i=1 1 p i ) and [69,Theorem 2] in the case when α ∈ ( n p , 1) ∩ (0, n i=1 1 p i ) can be deduced from Theorem 3.13(i) with X := L 1 (R n ) or X := L p ′ n p ′ α+n (R n ) and p ∈ (n, ∞) (This is indeed a special case of Theorem 4.7). To prove this claim, we first show that…”

Section: Morrey Spacesmentioning

confidence: 93%

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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Section: Morrey Spacesmentioning

confidence: 93%

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Chen¹,

Jia²,

Yang³

2022

Preprint

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“…In [10], authors studied Pólya-Szegö-type inequalities and Grüss-type inequalities with the help of ðk, ψÞ-proportional fractional operators. In recent years, many researchers have been working in the direction of estimating the fractional version of various inequalities [13][14][15][16][17][18][19] and the references given there.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev-Type Inequalities Involving ( $k, ψ$ )-Proportional Fractional Integral Operators

Yewale

Pachpatte

Aljaaidi

2022

Journal of Function Spaces

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Expanding the analytical aspect of mathematics enables researchers to study more cosmic phenomena, especially with regard to the applied sciences related to fractional calculus. In the present paper, we establish some Chebyshev-type inequalities in the case synchronous functions. In order to achieve our goals, we use k , ψ -proportional fractional integral operators. Moreover, we present some special cases.

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Boundedness of fractional integrals on ball Campanato-type function spaces

Chen

Jia

Yang

2023

Bulletin des Sciences Mathématiques

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Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

Abstract: In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.

Cited by 3 publications

References 30 publications

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Chebyshev-Type Inequalities Involving ( $k, ψ$ )-Proportional Fractional Integral Operators

Boundedness of fractional integrals on ball Campanato-type function spaces

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Boundedness for the Modified Fractional Integral Operator from Mixed Morrey Spaces to the Bounded Mean Oscillation Space and Lipschitz Spaces

Abstract: In this paper, we establish the boundedness of the modified fractional integral operator from mixed Morrey spaces to the bounded mean oscillation space and Lipschitz spaces, respectively.

Cited by 3 publications

References 30 publications

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Boundedness of Fractional Integrals on Ball Campanato-Type Function Spaces

Chebyshev-Type Inequalities Involving ( k , ψ )-Proportional Fractional Integral Operators

Boundedness of fractional integrals on ball Campanato-type function spaces

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Product

Resources

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Chebyshev-Type Inequalities Involving ( $k, ψ$ )-Proportional Fractional Integral Operators