On inclusion relation between weak Morrey spaces and Morrey spaces

2018 ◽  
Vol 168 ◽  
pp. 27-31
Author(s):  
Hendra Gunawan ◽  
Denny Ivanal Hakim ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Inclusion Relation ◽  
Weak Morrey Spaces

scholarly journals Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Xukui Shao ◽  
Shuangping Tao
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Variable Kernel ◽  
Fractional Integral Operators ◽  
Weak Type Estimates ◽  
Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

Weak Morrey spaces with applications

2017 ◽  
Vol 291 (1) ◽  
pp. 178-186 ◽  
Author(s):  
Yoshihiro Sawano ◽  
Saad R. El-Shabrawy
Keyword(s):  
Morrey Spaces ◽  
Weak Morrey Spaces

scholarly journals Third Version of Weak Orlicz–Morrey Spaces and Its In-clusion Properties

2019 ◽  
Vol 4 (2) ◽  
pp. 257-262
Author(s):  
Al Azhary Masta ◽  
Siti Fatimah ◽  
Muhammad Taqiyuddin
Keyword(s):  
Morrey Space ◽  
Necessary Conditions ◽  
Orlicz Spaces ◽  
Morrey Spaces ◽  
The Third ◽  
Inclusion Relations ◽  
Sufficient And Necessary Conditions ◽  
Weak Morrey Spaces

Orlicz–Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are  three  versions  of  Orlicz–Morrey  spaces.  In  this  article,  we discussed  the  third  version  of  weak  Orlicz–Morrey  space, which is an enlargement of third version of (strong) Orlicz– Morrey space. Similar to its first version and second version, the third version of weak Orlicz-Morrey space is considered as  a  generalization  of  weak  Orlicz  spaces,  weak  Morrey spaces,  and  generalized  weak  Morrey  spaces.  This  study investigated  some  properties  of the third  version of weak Orlicz–Morrey spaces, especially the sufficient and necessary conditions for inclusion relations between two these spaces. One of the keys to get our result is to estimate the quasi- norm of characteristics function of open balls in ℝ.

scholarly journals Wavelets, Sobolev Multipliers, and Application to Schrödinger Type Operators with Nonsmooth Potentials

2013 ◽  
Vol 2013 ◽  
pp. 1-22
Author(s):  
Pengtao Li ◽  
Qixiang Yang ◽  
Yueping Zhu
Keyword(s):  
Morrey Spaces ◽  
Type Operator ◽  
Inclusion Relation ◽  
Multiplier Space ◽  
Schrödinger Type Operator ◽  
Meyer Wavelets ◽  
Schrödinger Type Operators

We employ Meyer wavelets to characterize multiplier spaceXr,pt(ℝn)without using capacity. Further, we introduce logarithmic Morrey spacesMr,pt,τ(ℝn)to establish the inclusion relation between Morrey spaces and multiplier spaces. By fractal skills, we construct a counterexample to show that the scope of the indexτofMr,pt,τ(ℝn)is sharp. As an application, we consider a Schrödinger type operator with potentials inMr,pt,τ(ℝn).

scholarly journals Inclusion Properties of The Homogeneous Herz-Morrey

CAUCHY ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 117-121
Author(s):  
Hairur Rahman
Keyword(s):  
Homogeneous Spaces ◽  
Morrey Spaces ◽  
Inclusion Relation ◽  
Inclusion Properties

In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces and the homogeneous weak homogeneous spaces. We also studied the inclusion relation between those spaces.

scholarly journals Inclusion Properties of The Homogeneous Herz-Morrey Spaces With Variable Exponent

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 22-27
Author(s):  
Hairur Rahman
Keyword(s):  
Variable Exponent ◽  
Homogeneous Spaces ◽  
Morrey Spaces ◽  
Inclusion Relation ◽  
Inclusion Properties

In this paper, we have discussed about the inclusion properties of the homogeneous Herz-Morrey spaces with variable exponent and the weak homogeneous spaces with variable exponent. We also studied the inclusion relation between those spaces.

scholarly journals Pointwise Multipliers on Weak Morrey Spaces

2020 ◽  
Vol 8 (1) ◽  
pp. 363-381
Author(s):  
Ryota Kawasumi ◽  
Eiichi Nakai
Keyword(s):  
Growth Condition ◽  
Lebesgue Space ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Pointwise Multipliers ◽  
Weak Lebesgue Space ◽  
Weak Morrey Spaces

Abstract We consider generalized weak Morrey spaces with variable growth condition on spaces of homogeneous type and characterize the pointwise multipliers from a generalized weak Morrey space to another one. The set of all pointwise multipliers from a weak Lebesgue space to another one is also a weak Lebesgue space. However, we point out that the weak Morrey spaces do not always have this property just as the Morrey spaces not always.

scholarly journals Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2754
Author(s):  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Banach Lattices ◽  
Complete Picture ◽  
Pointwise Multiplier ◽  
Pointwise Multipliers ◽  
Vector Valued ◽  
Weak Morrey Spaces

The spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the first author’s papers written in 1997 and 2000, as well as Lemarié-Rieusset’s 2013 paper. As a corollary, the main result in the present paper shows that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the present paper is to provide a complete picture of the pointwise multiplier spaces.

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