Lp-Lq boundedness of continuous linear operators on smooth manifolds
Sánchez D.C. Kumar V. Ruzhansky M. Tokmagambetov N.
July 2025Birkhauser
Annals of Functional Analysis
2025#16Issue 3
In this paper, we study the boundedness of global continuous linear operators on smooth manifolds. Using the notion of a global symbol, we extend a classical condition of Hörmander type to guarantee the Lp-Lq-boundedness of global operators. Our approach links the mapping properties of continuous linear operators on smooth manifolds with the Lp-estimates of eigenfunctions of operators including a variety of examples, harmonic oscillators, anharmonic oscillators, etc. First, we investigate Lp-boundedness of pseudo-multipliers in the setting of Hörmander–Mihlin type conditions. We also prove L∞-BMO estimates for pseudo-multipliers. Later, we concentrate our investigation to settle Lp-Lq boundedness of the Fourier multipliers and pseudo-multipliers operators for the range 1
Continuous linear operator , Hausdorff–Young–Paley inequality , Non-linear partial differential equation , Nonharmonic analysis
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Department of Mathematics: Analysis Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematics, Queen Mary University of London, London, United Kingdom
Centre de Recerca Matemática, Edifici C, Campus Bellaterra, Barcelona, Bellaterra, 08193, Spain
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Department of Mathematics: Analysis Logic and Discrete Mathematics
School of Mathematics
Centre de Recerca Matemática
Institute of Mathematics and Mathematical Modeling
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