Abstract
We introduce weighted amalgam-type spaces and analyze their relations with some known spaces. Integrability results for the Fourier transform of a function with the derivative from one of those spaces are proved. The obtained results are applied to the integrability of trigonometric series with the sequence of coefficients of bounded variation.
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Dedicated to 80th anniversary of the Corresponding Member of NAS of Ukraine V. Ya. Gutlyanskii
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 18, No. 2, pp. 179–195, April–June, 2021.
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Liflyand, E. Fourier transforms on weighted amalgam-type spaces. J Math Sci 258, 290–302 (2021). https://doi.org/10.1007/s10958-021-05547-4
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DOI: https://doi.org/10.1007/s10958-021-05547-4