Uniform convergence and integrability of Fourier integrals

作者：Dyachenko Mikhail; Liflyand Elijah; Tikhonov Sergey^*

来源：Journal of Mathematical Analysis and Applications, 2010, 372(1): 328-338.

DOI：10.1016/j.jmaa.2010.06.023

• Fourier integrals
• Uniform convergence
• Weighted norm inequalities
• General monotone functions

Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on L(p)-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.

• 出版日期2010-12-1