Fourier inequalities in Morrey and Campanato spaces
Debernardi Pinos A. Nursultanov E. Tikhonov S.
1 October 2024Academic Press Inc.
Journal of Functional Analysis
2024#287Issue 7
We study norm inequalities for the Fourier transform, namely, ‖fˆ‖X≲‖f‖Y, where X is either a Morrey or Campanato space and Y is an appropriate function space. In the case of the Morrey space we sharpen the estimate ‖fˆ‖M≲‖f‖L, s≥2, [Formula presented]. We also show that (0.1) does not hold when both X and Y are Morrey spaces. If X is a Campanato space, we prove that (0.1) holds for Y being the truncated Lebesgue space.
Campanato spaces , Fourier inequalities , Morrey spaces
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Universitat Autònoma de Barcelona, Departament de Matemàtiques, Campus de Bellaterra, Edifici C, Bellaterra (Barcelona), 08193, Spain
Lomonosov Moscow State University (Kazakh Branch), Gumilyov Eurasian National University, Munatpasova 7, Astana, 010010, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Pushkin St. 125, Almaty, 050010, Kazakhstan
ICREA, Pg. Lluís Companys 23, Barcelona, 08010, Spain
Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Bellaterra (Barcelona), 08193, Spain
Universitat Autònoma de Barcelona
Lomonosov Moscow State University (Kazakh Branch)
Institute of Mathematics and Mathematical Modeling
ICREA
Centre de Recerca Matemàtica
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