B. G. Vakulov, Yu. E. Drobotov, “Variable order Riesz potential over <nobr>$\mathbb{\dot{R}}^n$</nobr> on weighted generalized variable Hölder spaces”, Sib. Èlektron. Mat. Izv., 2017, Volume 14,Pages <nobr>647

This article is cited 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. Vakulov^a, Yu. E. Drobotov^abc

^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.

UDC: 517.5

MSC: 31B10

Received July 19, 2016, published July 19, 2017

DOI: 10.17377/semi.2017.14.056