On the equivalence of the K-functional and the modulus of continuity on the Morrey spaces

Abstract In this note, the Morrey spaces and the Sobolev–Morrey spaces are considered. In particular, the K -functional with respect to these spaces is estimated from above and below. As an application, we characterize the Nikol’skii–Besov–Morrey spaces via real interpolation.

[1]  O. V. Besov,et al.  Integral representations of functions and imbedding theorems , 1978 .

[2]  D. Haroske,et al.  On Sobolev and Franke–Jawerth embeddings of smoothness Morrey spaces , 2014 .

[3]  Y. Sawano,et al.  The Fatou Property of Block Spaces , 2014, 1404.2688.

[4]  Dachun Yang,et al.  COMPLEX INTERPOLATION ON BESOV-TYPE AND TRIEBEL–LIZORKIN-TYPE SPACES , 2013 .

[5]  L. Vega,et al.  Non interpolation in Morrey-Campanato and block spaces , 1999 .

[6]  C. Bennett,et al.  Interpolation of operators , 1987 .

[7]  P. Lemarié–Rieusset.  Erratum to: Multipliers and Morrey Spaces , 2014 .

[8]  Y. Sawano.  Theory of Besov Spaces , 2018 .

[9]  H. Triebel,et al.  Morrey spaces, their duals and preduals , 2015 .

[10]  L. Vega,et al.  Corrigenda to "Unique continuation for Schrödinger operators" and a remark on intepolation of Morrey spaces , 1995 .

[11]  Henggeng Wang.  Decomposition for Morrey type Besov–Triebel spaces , 2009 .

[12]  Hitoshi Tanaka,et al.  Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces , 2007 .

[13]  Y. Netrusov.  Some imbedding theorems for spaces of Besov-Morrey type , 1987 .

[14]  V. Burenkov,et al.  Description of interpolation spaces for local Morrey-type spaces , 2010 .

[15]  Charles B. Morrey,et al.  On the solutions of quasi-linear elliptic partial differential equations , 1938 .

[16]  Y. Sawano,et al.  Generalized Morrey Spaces – Revisited , 2017 .

[17]  P. Lemarié–Rieusset.  Multipliers and Morrey Spaces , 2013 .

[18]  Yoshihiro Sawano,et al.  Generalized Morrey spaces and trace operator , 2016, 1605.08500.

[19]  D. Haroske,et al.  Continuous embeddings of Besov-Morrey function spaces , 2012 .

[20]  Y. Sawano,et al.  Interpolation of generalized Morrey spaces , 2016 .

[21]  Y. Sawano,et al.  Calderón’s First and Second Complex Interpolations of Closed Subspaces of Morrey Spaces , 2017 .

[22]  Y. Sawano.  A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces , 2009 .

[23]  M. Rosenthal.  Local means, wavelet bases and wavelet isomorphisms in Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces , 2013 .

[24]  Dachun Yang,et al.  Dual Properties of Triebel-Lizorkin-Type Spaces and their Applications , 2011 .

[25]  Y. Sawano.  WAVELET CHARACTERIZATION OF BESOV-MORREY AND TRIEBEL-LIZORKIN-MORREY SPACES , 2008 .

[26]  H. Kozono,et al.  Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data , 1994 .

[27]  W. Sickel,et al.  Interpolation of Morrey-Campanato and related smoothness spaces , 2014, 1406.0906.

[28]  Y. Sawano.  Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains , 2010 .

[29]  Y. Sawano,et al.  Approximation by trigonometric polynomials in variable exponent Morrey spaces , 2019 .

[30]  D. Haroske,et al.  Embeddings of Besov–Morrey spaces on bounded domains , 2013 .

[31]  Jingshi Xu,et al.  Some properties of Morrey type Besov–Triebel spaces , 2005 .

[32]  Y. Sawano,et al.  Complex interpolation and Calderón–Mityagin couples of Morrey spaces , 2019, Analysis & PDE.