hardy type operators
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2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko

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.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amjad Hussain ◽  
Naqash Sarfraz ◽  
Ilyas Khan ◽  
Abdelaziz Alsubie ◽  
Nawaf N. Hamadneh

AbstractIn this paper, we obtain some inequalities about commutators of a rough p-adic fractional Hardy-type operator on Herz-type spaces when the symbol functions belong to two different function spaces.


2021 ◽  
Author(s):  
Tomasz Kiwerski ◽  
Paweł Kolwicz ◽  
Lech Maligranda

2020 ◽  
Vol 100 (4) ◽  
pp. 26-32
Author(s):  
N.T. Bekbayev ◽  
◽  
K.S. Tulenov ◽  
◽  
◽  
...  

We study boundedness properties of the classical (singular) Hilbert transform (Hf)(t) = p.v.1/π \int_R f(s)/(t − s)ds acting on Marcinkiewicz spaces. The Hilbert transform is a linear operator which arises from the study of boundary values of the real and imaginary parts of analytic functions. Questions involving the H arise therefore from the utilization of complex methods in Fourier analysis, for example. In particular, the H plays the crucial role in questions of norm-convergence of Fourier series and Fourier integrals. We consider the problem of what is the least rearrangement-invariant Banach function space F(R) such that H : Mφ(R) → F(R) is bounded for a fixed Marcinkiewicz space Mφ(R). We also show the existence of optimal rearrangement-invariant Banach function range on Marcinkiewicz spaces. We shall be referring to the space F(R) as the optimal range space for the operator H restricted to the domain Mφ(R) ⊆ Λϕ0(R). Similar constructions have been studied by J.Soria and P.Tradacete for the Hardy and Hardy type operators [1]. We use their ideas to obtain analogues of their some results for the H on Marcinkiewicz spaces.


2020 ◽  
Vol 77 (1) ◽  
pp. 1-29
Author(s):  
Qinxiu Sun ◽  
Xiao Yu ◽  
Hongliang Li

2020 ◽  
Vol 107 (5-6) ◽  
pp. 1002-1013
Author(s):  
Qinxiu Sun ◽  
Hongliang Li

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