Abstract:
Sufficient conditions for the weighted integrability of multiple multiplicative Fourier transforms of Bernstein–Szasz type involving integral moduli of continuity and of Zygmund type with an additional boundedness condition for $s$ fluctuations are given in the paper. The sharpness of Bernstein–Szasz type tests is proved under certain restrictions.
Keywords:multiplicative Fourier transform, weighted integrability, function with bounded $s$-fluctuation, Lipschitz classes.
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