Complex interpolation of the predual of Morrey spaces over measure spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Victor I. Burenkov ◽  
Denny I. Hakim ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano ◽  
Takuya Sobukawa ◽  
...  
Keyword(s):  
Radon Measure ◽  
Duality Theorem ◽  
Interpolation Method ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Block Spaces ◽  
Measure Spaces ◽  
Calderón Product

Abstract We prove that block spaces defined on {\mathbb{R}^{n}} with an arbitrary Radon measure, which are known to be the preduals of Morrey spaces, are closed under the first and the second complex interpolation method. The proof of our main theorem uses the duality theorem in the complex interpolation method, the complex interpolation of certain closed subspaces of Morrey spaces, a characterization of the preduals of block spaces, and some formulas related to the Calderón product.

Interpolation of Morrey Spaces on Metric Measure Spaces

2014 ◽  
Vol 57 (3) ◽  
pp. 598-608 ◽  
Author(s):  
Yufeng Lu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Interpolation Method ◽  
Interpolation Theorem ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Metric Measure Spaces ◽  
Interpolation Methods ◽  
Measure Spaces

AbstractIn this article, via the classical complex interpolation method and some interpolation methods traced to Gagliardo, the authors obtain an interpolation theorem for Morrey spaces on quasimetric measure spaces, which generalizes some known results on ℝn.

scholarly journals Calderon's Complex Interpolation of Morrey Spaces

2020 ◽  
Vol 26 (1) ◽  
pp. 137-164
Author(s):  
Denny Hakim
Keyword(s):  
Interpolation Method ◽  
Interpolation Property ◽  
Interpolation Theorem ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Generalized Morrey Spaces ◽  
Definition Of

In this note we will discuss some results related to complex interpolation of Morreyspaces. We first recall the Riesz-Thorin interpolation theorem in Section 1.After that, we discuss a partial generalization of this theorem in Morrey spaces proved in \cite{St}.We also discuss non-interpolation property of Morrey spaces given in \cite{BRV99, RV}.In Section 3, we recall the definition of Calder\'on's complex interpolation method andthe description of complex interpolation of Lebesgue spaces.In Section 4, we discuss the description of complex interpolation of Morrey spaces given in\cite{CPP98, HS2, Lemarie, LYY}. Finally, we discuss the description of complex interpolationof subspaces of Morrey spaces in the last section.This note is a summary of the current research about interpolation of Morrey spaces,generalized Morrey spaces, and their subspaces in\cite{CPP98, HS, HS2, H, H4, Lemarie, LYY}.

scholarly journals Relatively Compact Sets in Variable Exponent Morrey Spaces on Metric Spaces

2021 ◽  
Vol 18 (6) ◽  
Author(s):  
Rovshan A. Bandaliyev ◽  
Przemysław Górka ◽  
Vagif S. Guliyev ◽  
Yoshihiro Sawano
Keyword(s):  
Variable Exponent ◽  
Metric Spaces ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Compact Sets ◽  
Totally Bounded ◽  
Measure Spaces ◽  
Points Of View ◽  
Bounded Sets

AbstractWe study a characterization of the precompactness of sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally bounded sets are characterized from several points of view for the case of variable exponent Morrey spaces over metric measure spaces. This characterization is new in the case of constant exponents.

Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

2013 ◽  
Vol 318 ◽  
pp. 100-107
Author(s):  
Zhen Shen ◽  
Biao Wang ◽  
Hui Yang ◽  
Yun Zheng
Keyword(s):  
Data Exchange ◽  
Shape Function ◽  
Interpolation Method ◽  
Matching Condition ◽  
Optimal Interpolation ◽  
Complex Interpolation ◽  
Interpolation Function ◽  
Interpolation Methods ◽  
Interpolation Accuracy ◽  
Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

scholarly journals Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces

2018 ◽  
Vol 12 (4) ◽  
pp. 629-639
Author(s):  
B. K. Dass ◽  
◽  
Namita Sharma ◽  
Rashmi Verma ◽  
Keyword(s):  
Perfect Codes ◽  
Block Spaces ◽  
Golay Codes

A remark on modified Morrey spaces on metric measure spaces

2018 ◽  
Vol 47 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Yoshihiro SAWANO ◽  
Tetsu SHIMOMURA ◽  
Hitoshi TANAKA}
Keyword(s):  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Measure Spaces

Weighted fractional Hardy operators and their commutators on generalized Morrey spaces over quasi-metric measure spaces

2021 ◽  
Vol 24 (6) ◽  
pp. 1643-1669
Author(s):  
Natasha Samko
Keyword(s):  
Upper Bound ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Target Space ◽  
Metric Measure Spaces ◽  
Generalized Morrey Spaces ◽  
Hardy Type ◽  
Measure Spaces ◽  
Hardy Operators ◽  
Hardy Type Operators

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.

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