scholarly journals The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Takeshi Iida
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Morrey Spaces ◽  
Weighted Morrey Spaces ◽  
Type Spaces ◽  
Multilinear Maximal Function ◽  
Multilinear Maximal Operator ◽  
Littlewood Maximal Operator

The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function.

scholarly journals Vector-Valued Inequalities in the Morrey Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Hua Wang
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Growth Function ◽  
Morrey Spaces ◽  
Doubling Condition ◽  
Littlewood Maximal Function ◽  
Weighted Morrey Spaces ◽  
Weak Type Estimates ◽  
Type Spaces ◽  
Vector Valued

We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spacesLp,κ(w)when1≤p<∞and0<κ<1, and in the generalized Morrey spacesLp,Φfor1≤p<∞, whereΦis a growth function on(0,∞)satisfying the doubling condition.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

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.

scholarly journals Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano ◽  
Idha Sihwaningrum
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Generalized Fractional Integral ◽  
Littlewood Maximal Operator ◽  
Generalized Fractional Integral Operators

We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

Generalized Hausdorff capacities and their applications

2018 ◽  
Vol 25 (3) ◽  
pp. 381-396
Author(s):  
Xinlei He ◽  
Wen Yuan
Keyword(s):  
Morrey Spaces ◽  
Lebesgue Spaces ◽  
Strong Subadditivity ◽  
Weighted Morrey Spaces ◽  
Choquet Capacity ◽  
Power Set ◽  
Dyadic Cubes ◽  
Set Function ◽  
Littlewood Maximal Operator ◽  
Equivalent Variant

AbstractLet {\mathfrak{P}({\mathbb{R}^{n}})} be the power set of {\mathbb{R}^{n}} and let {\varphi:\mathfrak{P}({\mathbb{R}^{n}})\rightarrow[0,\infty]} be a set function. In this paper, the authors introduce a class of generalized Hausdorff capacities {H_{\varphi}} with respect to φ. Some basic properties of {H_{\varphi}} including the strong subadditivity are obtained. An equivalent variant of {H_{\varphi}} defined via dyadic cubes is also introduced and proved to be Choquet capacity. The authors then prove the boundedness of some maximal operators, such as the Hardy–Littlewood maximal operator, on Lebesgue spaces with respect to {H_{\varphi}}. As an application, the predual spaces of weighted Morrey spaces are described via these capacities.

scholarly journals Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 1000-1014
Author(s):  
Suixin He ◽  
◽  
Shuangping Tao
Keyword(s):  
Bounded Domain ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Space ◽  
Homogeneous Spaces ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Generalized Morrey Space ◽  
Fractional Integral Operators ◽  
Littlewood Maximal Operator

<abstract><p>The aim of this paper is to obtain the boundedness of some operator on grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ over non-homogeneous spaces, where $ G\subset $ $ \mathbb{R}^{n} $ is a bounded domain. Under assumption that functions $ \varphi $ and $ \phi $ satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and $ \theta $-type Calderón-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $. Moreover, the boundedness of commutator $ [b, T^{G}_{\theta}] $ which is generated by $ \theta $-type Calderón-Zygmund operator $ T_{\theta} $ and $ b\in\mathrm{RBMO}(\mu) $ on spaces $ \mathcal{L}^{p), \varphi, \phi}_{\mu}(G) $ is also established.</p></abstract>

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