Uniform convergence and integrability of multiplicative Fourier transforms

作者：Volosivets S S^*; Golubov B I

来源：Mathematical Notes, 2015, 98(1-2): 53-67.

DOI：10.1134/S0001434615070056

• multiplicative Fourier transform
• weighted integrability of Fourier transforms
• Lipschitz class
• Lipschitz-Besov space
• Herz space
• Dirichlet kernel
• Holder's inequality
• Hardy's inequality
• Minkowski's inequality

For multiplicative Fourier transforms, analogs of results obtained by R. P. Boas, F. Moricz, M. I. D'yachenko, I. P. Liflyand, and S. Yu. Tikhonov and dealing with conditions for the uniform convergence and weighted integrability with power weight of classical Fourier transforms as well as conditions for these transforms to belong to Lipschitz classes are proved. Certain results of C. W. Onneweer concerning conditions for multiplicative Fourier transforms to belong to Lipschitz-Besov and Herz spaces are also generalized.

• 出版日期2015-7