Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals | Zendy

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Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integrals

Author(s) -

Damiano Foschi

Publication year - 2005

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2005.4.569

Subject(s) - trigonometry , mathematics , connection (principal bundle) , trigonometric integral , operator (biology) , trigonometric functions , constant (computer programming) , trigonometric polynomial , pure mathematics , mathematical analysis , phase (matter) , physics , quantum mechanics , computer science , biochemistry , chemistry , geometry , repressor , transcription factor , gene , programming language

We discuss the asymptotic behaviour for the best constant in L^p-L^qestimates for trigonometric polinomials and for an integral operator which isrelated to the solution of inhomogeneous Schrodinger equations. This gives usan opportunity to review some basic facts about oscillatory integrals and themethod of stationary phase, and also to make some remarks in connection withStrichartz estimates.

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