Complex interpolation of variable Morrey spaces

2021 ◽  
Author(s):  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation

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.

COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES

2013 ◽  
Vol 11 (05) ◽  
pp. 1350021 ◽  
Author(s):  
DACHUN YANG ◽  
WEN YUAN ◽  
CIQIANG ZHUO
Keyword(s):  
Morrey Spaces ◽  
Schwartz Space ◽  
Complex Interpolation ◽  
Schwartz Functions ◽  
Type Spaces ◽  
Besov Type Spaces

Let θ ∈ (0, 1), s0, s1 ∈ ℝ, τ0, τ1 ∈ [0, ∞), p0, p1 ∈ (0, ∞), q0, q1 ∈ (0, ∞], s = s0(1 - θ) + s1θ, τ = τ0(1-θ) + τ1θ, [Formula: see text] and [Formula: see text]. In this paper, under the restriction [Formula: see text], the authors establish the complex interpolation, on Triebel–Lizorkin-type spaces, that [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz functions in [Formula: see text]. Similar results on Besov-type spaces and Besov–Morrey spaces are also presented. As a corollary, the authors obtain the complex interpolation for Morrey spaces that, for all 1 < p0 ≤ u0 < ∞, 1 < p1 ≤ u1 < ∞ and 1 < p ≤ u < ∞ such that [Formula: see text], [Formula: see text] and p0u1 = p1u0, [Formula: see text], where [Formula: see text] denotes the closure of the Schwartz space in [Formula: see text]. It is known that, if p0u1 ≠ p1u0, these conclusions on Morrey spaces may not be true.

Complex interpolation and Calderón–Mityagin couples of Morrey spaces

2019 ◽  
Vol 12 (7) ◽  
pp. 1711-1740 ◽  
Author(s):  
Mieczysław Mastyło ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation

scholarly journals Complex interpolation of vanishing Morrey spaces

2020 ◽  
Vol 11 (3) ◽  
pp. 643-661
Author(s):  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation

Complex interpolation of various subspaces of Morrey spaces

2020 ◽  
Vol 63 (5) ◽  
pp. 937-964 ◽  
Author(s):  
Denny Ivanal Hakim ◽  
Yoshihiro Sawano
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation

scholarly journals Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains

2020 ◽  
Vol 8 (1) ◽  
pp. 268-304
Author(s):  
Ciqiang Zhuo ◽  
Marc Hovemann ◽  
Winfried Sickel
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation ◽  
Bounded Domains

AbstractIn this article the authors study complex interpolation of Sobolev-Morrey spaces and their generalizations, Lizorkin-Triebel-Morrey spaces. Both scales are considered on bounded domains. Under certain conditions on the parameters the outcome belongs to the scale of the so-called diamond spaces.

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}.

Complex interpolation of Morrey spaces

Morrey Spaces ◽  
2020 ◽  
pp. 323-363
Author(s):  
Yoshihiro Sawano ◽  
Giuseppe Di Fazio ◽  
Denny Ivanal Hakim
Keyword(s):  
Morrey Spaces ◽  
Complex Interpolation
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