Boundedness of Riesz-Type Potential Operators on Variable Exponent Herz–Morrey Spaces

2018 ◽  
Vol 69 (9) ◽  
pp. 1379-1392
Author(s):  
J.-L. Wu
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Potential Operators ◽  
Type Potential

Maximal and Potential Operators in Variable Exponent Morrey Spaces

2008 ◽  
Vol 15 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Alexandre Almeida ◽  
Javanshir Hasanov ◽  
Stefan Samko
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Bmo Space ◽  
Sobolev Type ◽  
Potential Operator ◽  
Variable Order ◽  
Potential Operators ◽  
Open Set ◽  
Limiting Case ◽  
Littlewood Maximal Operator

Abstract We prove the boundedness of the Hardy–Littlewood maximal operator on variable Morrey spaces 𝐿𝑝(·), λ(·)(Ω) over a bounded open set Ω ⊂ ℝ𝑛 and a Sobolev type 𝐿𝑝(·), λ(·) → 𝐿𝑞(·), λ(·)-theorem for potential operators 𝐼 α(·), also of variable order. In the case of constant α, the limiting case is also studied when the potential operator 𝐼 α acts into BMO space.

scholarly journals Boundedness of the maximal, potential and singular operators in the generalized variable exponent Morrey spaces

2010 ◽  
Vol 107 (2) ◽  
pp. 285 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Javanshir J. Hasanov ◽  
Stefan G. Samko
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Morrey Spaces ◽  
Variable Order ◽  
General Function ◽  
Singular Operators ◽  
Potential Operators ◽  
Type Integral ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

We consider generalized Morrey spaces ${\mathcal M}^{p(\cdot),\omega}(\Omega)$ with variable exponent $p(x)$ and a general function $\omega (x,r)$ defining the Morrey-type norm. In case of bounded sets $\Omega \subset {\mathsf R}^n$ we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev-Adams type ${\mathcal M}^{p(\cdot),\omega} (\Omega)\rightarrow {\mathcal M}^{q(\cdot),\omega} (\Omega)$-theorem for the potential operators $I^{\alpha(\cdot)}$, also of variable order. The conditions for the boundedness are given it terms of Zygmund-type integral inequalities on $\omega(x,r)$, which do not assume any assumption on monotonicity of $\omega(x,r)$ in $r$.

scholarly journals Riesz type potential operators in generalized grand Morrey spaces

2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Humberto Rafeiro
Keyword(s):  
Morrey Spaces ◽  
Potential Operators ◽  
Type Potential

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

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