TY - JOUR
T1 - On the convolution operator in Morrey spaces
AU - Nursultanov, Erlan D.
AU - Suragan, Durvudkhan
N1 - Funding Information:
We would like to thank the reviewers for their thoughtful comments and efforts towards improving our paper. This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08856479 ). The authors were also supported by the NU grant 240919FD3901 . No new data was collected or generated during the course of research.
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/11/1
Y1 - 2022/11/1
N2 - This paper is devoted to the study of upper bounds for the norm of the convolution operator in Morrey spaces. The spaces Mp,qα, which cover the classical Morrey spaces, are introduced. Moreover, their embedding properties are investigated, and their interpolation properties are described. Young-O'Neil type inequalities in Morrey spaces are proved. New results on the boundedness of Riesz's potential in Morrey spaces are established.
AB - This paper is devoted to the study of upper bounds for the norm of the convolution operator in Morrey spaces. The spaces Mp,qα, which cover the classical Morrey spaces, are introduced. Moreover, their embedding properties are investigated, and their interpolation properties are described. Young-O'Neil type inequalities in Morrey spaces are proved. New results on the boundedness of Riesz's potential in Morrey spaces are established.
KW - Convolution operator
KW - Interpolation theorems
KW - Morrey spaces
KW - Riesz's potential
KW - Young-O'Neil inequality
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U2 - 10.1016/j.jmaa.2022.126357
DO - 10.1016/j.jmaa.2022.126357
M3 - Article
AN - SCOPUS:85131397490
SN - 0022-247X
VL - 515
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
M1 - 126357
ER -