RKH spaces of Brownian type defined by Cesàro–Hardy operators

In this paper, we find sufficient conditions on general Young functions $(\Phi, \Psi)$ and the functions $(\varphi_1,\varphi_2)$ ensuring that the weighted Hardy operators $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ are of strong type from a local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ into another local generalized Orlicz-Morrey space $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$. We also obtain the boundedness of the commutators of $A_\omega^\alpha$ and ${\mathcal A}_\omega^\alpha$ from $M^{0,\,loc}_{\Phi,\,\varphi_1}(\mathbb R^n)$ to $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.

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CBMO estimates for multilinear Hardy operators

Acta Mathematica Sinica English Series ◽

10.1007/s10114-010-8603-8 ◽

2010 ◽

Vol 26 (7) ◽

pp. 1245-1254 ◽

Cited By ~ 2

Author(s):

Shan Zhen Lu ◽

Fa You Zhao

Keyword(s):

Hardy Operators

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Sharp bounds for Hardy operators on product spaces

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30759-8 ◽

2018 ◽

Vol 38 (2) ◽

pp. 441-449

Author(s):

Mingquan WEI ◽

Dunyan YAN

Keyword(s):

Product Spaces ◽

Sharp Bounds ◽

Hardy Operators

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Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2021-0071 ◽

2021 ◽

Vol 24 (6) ◽

pp. 1643-1669

Author(s):

Natasha Samko

Keyword(s):

Upper Bound ◽

Morrey Space ◽

Morrey Spaces ◽

Target Space ◽

Metric Measure Spaces ◽

Generalized Morrey Spaces ◽

Hardy Type ◽

Measure Spaces ◽

Hardy Operators ◽

Hardy Type Operators

Abstract We study commutators of weighted fractional Hardy-type operators within the frameworks of local generalized Morrey spaces over quasi-metric measure spaces for a certain class of “radial” weights. Quasi-metric measure spaces may include, in particular, sets of fractional dimentsions. We prove theorems on the boundedness of commutators with CMO coefficients of these operators. Given a domain Morrey space 𝓛 p,φ (X) for the fractional Hardy operators or their commutators, we pay a special attention to the study of the range of the exponent q of the target space 𝓛 q,ψ (X). In particular, in the case of classical Morrey spaces, we provide the upper bound of this range which is greater than the known Adams exponent.

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