scholarly journals Maximal Operator in Variable Exponent Generalized Morrey Spaces on Quasi-metric Measure Space

2015 ◽  
Vol 13 (3) ◽  
pp. 1151-1165 ◽  
Author(s):  
Vagif S. Guliyev ◽  
Stefan G. Samko
Keyword(s):  
Maximal Operator ◽  
Measure Space ◽  
Variable Exponent ◽  
Morrey Spaces ◽  
Metric Measure Space ◽  
Generalized Morrey Spaces

scholarly journals Parameter θ -Type Marcinkiewicz Integral on Nonhomogeneous Weighted Generalized Morrey Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Guanghui Lu
Keyword(s):  
Measure Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Metric Measure Space ◽  
Marcinkiewicz Integral ◽  
Generalized Morrey Space ◽  
Generalized Morrey Spaces ◽  
Formula Type

Let X , d , μ be a nonhomogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. In this setting, the author proves that parameter θ -type Marcinkiewicz integral M θ ρ is bounded on the weighted generalized Morrey space L p , ϕ , τ ω for p ∈ 1 , ∞ . Furthermore, the boudedness of M θ ρ on weak weighted generalized Morrey space W L p , ϕ , τ ω is also obtained.

GENERALIZED MORREY SPACES OVER NONHOMOGENEOUS METRIC MEASURE SPACES

2016 ◽  
Vol 103 (2) ◽  
pp. 268-278 ◽  
Author(s):  
GUANGHUI LU ◽  
SHUANGPING TAO
Keyword(s):  
Integral Operator ◽  
Measure Space ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Marcinkiewicz Integral ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Measure Spaces ◽  
Definition Of ◽  
Marcinkiewicz Integral Operator

Let $({\mathcal{X}},d,\unicode[STIX]{x1D707})$ be a nonhomogeneous metric measure space satisfying the so-called upper doubling and the geometric doubling conditions. In this paper, the authors give the natural definition of the generalized Morrey spaces on $({\mathcal{X}},d,\unicode[STIX]{x1D707})$, and then investigate some properties of the maximal operator, the fractional integral operator and its commutator, and the Marcinkiewicz integral operator.

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 $r$.

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