$$L_p\rightarrow L_q$$ boundedness of Fourier multipliers

2025

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DOI 10.1007/s10476-025-00078-5
Data confidence 70 medium
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Abstract

Abstract This paper explores the boundedness of Fourier multipliers from $$L_p$$ L p to $$L_q$$ L q . We present new results that improve upon classical theorems due to Hörmander, Lizorkin, and Marcinkiewicz. In addition, we provide necessary conditions for the boundedness of Fourier multipliers. We introduce the concept of $$M$$ M -generalized monotone functions and sequences and derive criteria for the boundedness of Fourier multipliers corresponding to them.