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Uniform convergence and integrability of Fourier integrals |
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| Authors: | Mikhail Dyachenko |
| Affiliation: | a Moscow State University, Vorobe‘vy Gory, 119992, Russia b Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel c ICREA and Centre de Recerca Matemàtica, Apartat 50, 08193 Bellaterra, Barcelona, Spain |
| Abstract: | Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions. |
| Keywords: | Fourier integrals Uniform convergence Weighted norm inequalities General monotone functions |
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