Intermediate spaces on weak type discrete Morrey spaces
DOI:
https://doi.org/10.62918/hjma.v3i2.33Keywords:
discrete Morrey spaces, weak discrete Morrey spaces, inclusion, intermediate spacesAbstract
In this article we discuss inclusion between a discrete Morrey space and a weak discrete Morrey space as well as inclusion between two weak discrete Morrey spaces. By the inclusion properties of weak discrete Morrey spaces, we have intermediate spaces for the trivial case. Using the inclusion relation of discrete Morrey spaces and weak discrete Morrey spaces, we obtain that for the nontrivial case there is no weak discrete Morrey space between Banach pairs of weak discrete Morrey spaces except for the two weak discrete Morrey spaces itself.
References
D. R. Adams, Morrey spaces: Lecture Notes in Applied and Numerical Harmonic Analysis, Springer, Cham, 2015.
H. Gunawan, D. I. Hakim, M. Idris, Proper inclusions of Morrey spaces, Glasnik matematicki 53 (2018), no. 1, 143–151.
H. Gunawan, D. I. Hakim, M. Idris, On inclusion properties of discrete Morrey spaces, Georgian Math. J. 29 (2022) 37--44.
H. Gunawan, D. I. Hakim, K. M. Limanta, A. A. Masta, Inclusion properties of generalized Morrey spaces, Math. Nachr. 290 (2017) 332--340.
H. Gunawan, D. I. Hakim, E. Nakai, Y. Sawano, On inclusion relation between weak Morrey spaces and Morrey spaces, Nonlinear Anal. 168 (2018) 27--31.
H. Gunawan, E. Kikianty, C. Schwanke, Discrete Morrey spaces and their inclusion properties, Math. Nachr. 291 (2018) 1283--1296.
D. D. Haroske, L. Skrzypczak, Embeddings of weighted Morrey spaces, Math. Nachr. 290 (2017) 1066--1086.
D. D. Haroske, L. Skrzypczak, Morrey sequence spaces: Pitt’s theorem and compact embeddings, Constr. Approx. 51 (2020) 505--535.
E. Kikianty, C. Schwanke, Discrete morrey spaces are closed subspaces of their continuous counterparts, Banach Center Publ. 119 (2019), 223–231.
S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of linear operators, volume 54 of translations of mathematical monographs} American Mathematical Society, 1982.
P. G. Lemarié-Rieusset, Erratum to ``Multipliers and Morrey spaces'', Potential Anal. 41.4 (2014) 1359--1362.
Y. Lu, D. Yang, W. Yuan, Interpolation of Morrey spaces on metric measure spaces, Canad. Math. Bull. 57.3 (2014) 598--608.
M. Mastyło, Y. Sawano, Complex interpolation and Calderón-Mityagin couples of Morrey spaces, Anal. PDE 12.7 (2019) 1711--1740.
C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938) 126--166.
J. Peetre, On the theory of L_{p,lambda} spaces, J. Funct. Anal 4 (1969) 71--87.
L. C. Piccinini, Inclusioni tra spazi di Morrey, Boll. Un. Mat. Ital. 4.2 (1969) 95--99.
Y. Sawano, A non-dense subspace in M^p_q with 1
Y. Sawano, G. Di Fazio, D. I. Hakim, Morrey spaces: Introduction and Applications to Integral Operators and PDE's Vol. I, Monographs and Research Notes in Mathematics, Chapman & Hall CRC Press, Boca Raton, FL, 2020.
Y. Sawano, G. Di Fazio, D. I. Hakim, Morrey spaces: Introduction and Applications to Integral Operators and PDE's Vol. II, Monographs and Research Notes in Mathematics, Chapman & Hall CRC Press, Boca Raton, FL, 2020.
Y. Sawano, H. Tanaka, Morrey spaces for non-doubling measures. Acta Math. Sinica 21 (2005), no. 6, 1535--1544.
R. Yudatama, The Structure of Discrete Morrey Spaces and Their Intermediate Spaces, Master’s Program Thesis, Institut Teknologi Bandung, 2024.
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