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This article is cited in 1 scientific paper (total in 1 paper)
Real, complex and functional analysis
Variable order Riesz potential over $\mathbb{\dot{R}}^n$ on weighted generalized variable Hölder spaces
B. G. Vakulova, Yu. E. Drobotovabc a Vorovich Institute of Mathematics, Mechanics and Computer Sciences,
Milchakova str., 8a,
344090, Rostov-on-Don, Russia
b Azov Sea Research Fisheries Institute,
ul. Beregovaya, 21v,
344002, Rostov-on-Don, Russia
c SPE Vibrobit LLC,
ul. Kapustina, 8a,
344092, Rostov-on-Don, Russia
Abstract:
Theorems on the conditions for the spherical Riesz potential type operator to be bounded in the generalized Hölder spaces
are considered to develop results for the spatial case.
Due to applying stereographic projection, theorems on boundedness of the variable order multidimensional potential type operator
in the generalized variable Hölder spaces are proven.
Keywords:
fractional calculus, variable order, generalized Hölder space, Riesz potential.
Received July 19, 2016, published July 19, 2017
Citation:
B. G. Vakulov, Yu. E. Drobotov, “Variable order Riesz potential over $\mathbb{\dot{R}}^n$ on weighted generalized variable Hölder spaces”, Sib. Èlektron. Mat. Izv., 14 (2017), 647–656
Linking options:
https://www.mathnet.ru/eng/semr813 https://www.mathnet.ru/eng/semr/v14/p647
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