On generalised bessel potentials in weighted lebesgue space

The article considers the convolution type operator represented by the generalized Bessel potential. The action of the generalized Bessel potential in a special Lebesgue class of functions with power weight is studied. A theorem on the boundedness of the generalized Bessel potential in the weighed Lebesgue class is proved. It is also shown that the generalized Bessel potential in the weighted Lebesgue class of functions is a weak type operator in the sense of a norm constructed using a weighted distribution function. These results are an extension of the Hardy – Littlewood – Sobolev theory of fractional integration to the case of a generalized Bessel potential. Acknowledgements The work is supported of the Ministry of Education and Science of the Russian Federation on a state assignment FEGS-2020-0001.