# Weighted norm estimates for the Semyanistyi fractional integrals and Radon transforms

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Semyanistyis fractional integrals have come to analysis from integral geometry. They take functions on \$R^n\$ to functions on hyperplanes, commute with rotations, and have a nice behavior with respect to dilations. We obtain sharp inequalities for these integrals and the corresponding Radon transforms acting on \$L^p\$ spaces with a radial power weight. The operator norms are explicitly evaluated. Similar results are obtained for fractional integrals associated to \$k\$-plane transforms for any \$1\le k

Autor: Boris Rubin

Fuente: https://archive.org/