Integrability and Uniform Convergence of Multiplicative Transforms

For multiplicative Fourier transforms the analogues of the results of the papers (Dyachenko et al., J. Math. Anal. Appl., 372:328–338, 2010; Sampson and Tuy, Pac. J. Math., 75:519–537, 1978; Moricz, Stud. Math., 199:199–205, 2010; Liflyand and Tikhonov, C.R. Acad. Sci. Paris, Ser. 1, 346:1137–1142, 2008) on uniform convergence and integrability with power weights of classical Fourier transform are obtained. Some generalizations of the results of Onneweer (Lect. Notes., Math 939:106–121, 1981; Monatsh. Math., 97:297–310, 1984) on belonging of multiplicative Fourier transforms to Besov-Lipschitz or Herz spaces are stated.