scholarly journals Weighted multilinear p-adic Hardy operators and commutators

2017 ◽  
Vol 15 (1) ◽  
pp. 1623-1634
Author(s):  
Ronghui Liu ◽  
Jiang Zhou
Keyword(s):  
Morrey Spaces ◽  
Special Structure ◽  
Euclidean Spaces ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Hardy Operators

Abstract In this paper, the weighted multilinear p-adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p-adic Lebesgue spaces, and the product of p-adic central Morrey spaces, the product of p-adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p-adic Hardy operators on the product of p-adic central Morrey spaces. However, it’s worth mentioning that these results are different from that on Euclidean spaces due to the special structure of the p-adic fields.

scholarly journals Weighted multilinear Hardy operators and commutators

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Zun Wei Fu ◽  
Shu Li Gong ◽  
Shan Zhen Lu ◽  
Wen Yuan
Keyword(s):  
Necessary Conditions ◽  
Morrey Spaces ◽  
Bmo Space ◽  
Weight Functions ◽  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Sharp Estimates ◽  
Sufficient And Necessary Conditions ◽  
Hardy Operators

AbstractIn this paper, we introduce a type of weighted multilinear Hardy operators and obtain their sharp bounds on the product of Lebesgue spaces and central Morrey spaces. In addition, we obtain sufficient and necessary conditions of the weight functions so that the commutators of the weighted multilinear Hardy operators (with symbols in central BMO space) are bounded on the product of central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Riemann–Liouville and Weyl.

scholarly journals Boundedness ofp-Adic Hardy Operators and Their Commutators onp-Adic Central Morrey and BMO Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qing Yan Wu ◽  
Ling Mi ◽  
Zun Wei Fu
Keyword(s):  
Morrey Spaces ◽  
Sharp Bounds ◽  
Bmo Spaces ◽  
Hardy Operators

We obtain the sharp bounds ofp-adic Hardy operators onp-adic central Morrey spaces andp-adicλ-central BMO spaces, respectively. We also establish theλ-central BMO estimates for commutators ofp-adic Hardy operators onp-adic central Morrey spaces.

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

2004 ◽  
Vol 2 (1) ◽  
pp. 55-69 ◽  
Author(s):  
David E. Edmunds ◽  
Vakhtang Kokilashvili ◽  
Alexander Meskhi
Keyword(s):  
Variable Exponent ◽  
Homogeneous Type ◽  
Trace Inequality ◽  
Spaces Of Homogeneous Type ◽  
Weighted Inequality ◽  
Euclidean Spaces ◽  
Riesz Potentials ◽  
Lebesgue Spaces ◽  
Fractal Sets

A trace inequality for the generalized Riesz potentialsIα(x)is established in spacesLp(x)defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentialsIα(x)defined on fractal sets is derived.

scholarly journals Weighted Hardy operators in local generalized Orlicz-Morrey spaces

2021 ◽  
Vol 13 (2) ◽  
pp. 522-533
Author(s):  
C. Aykol ◽  
Z.O. Azizova ◽  
J.J. Hasanov
Keyword(s):  
Morrey Space ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Strong Type ◽  
Young Functions ◽  
Weighted Hardy Operators ◽  
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 $M^{0,\,loc}_{\Psi,\,\varphi_2}(\mathbb R^n)$.

Sharp bounds for Hardy operators on product spaces

2018 ◽  
Vol 38 (2) ◽  
pp. 441-449
Author(s):  
Mingquan WEI ◽  
Dunyan YAN
Keyword(s):  
Product Spaces ◽  
Sharp Bounds ◽  
Hardy Operators

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

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.

scholarly journals Sharp bounds for general commutators on weighted Lebesgue spaces

2012 ◽  
Vol 364 (3) ◽  
pp. 1163-1177 ◽  
Author(s):  
Daewon Chung ◽  
M. Cristina Pereyra ◽  
Carlos Perez
Keyword(s):  
Lebesgue Spaces ◽  
Sharp Bounds ◽  
Weighted Lebesgue Spaces

Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces

2020 ◽  
Vol 27 (3) ◽  
pp. 433-439
Author(s):  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Doubling Measure ◽  
Lebesgue Spaces ◽  
Grand Lebesgue Spaces ◽  
Measure Spaces

AbstractThe predual spaces of generalized grand Morrey spaces over non-doubling measure spaces are investigated. The case of the grand Lebesgue spaces is covered, which is also new. An example shows that the modification of Morrey spaces is essential.

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