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Adams-Guliyev type boundedness for the anisotropic Riesz potential on anisotropic generalized Morrey spaces

Adams-Guliyev type boundedness for the anisotropic Riesz potential
on anisotropic generalized Morrey spaces

M.S.Dzhabrailov1, S.Z.Khaligova2

1Azerbaijan State Pedagogical University, Baku, Azerbaijan
Mathematical faculty, Mathematical analysis
Az 1000, U.Hajibekov str. 34
2Azerbaijan State Pedagogical University, Baku, Azerbaijan
Mathematical faculty, Mathematical analysis
Az 1000, U.Hajibekov str. 34
tel.:(99450) 4031081 ,e-mail: seva.xaligova@hotmail.com

Let and with for For and denote the open parallelepiped centered at of side length for Let The anisotropic generalized Morrey space is defined of all functions by the finite norm

The following is a result of Spanne-Guliyev type for the anisotropic Riesz potential.
Theorem 1. Let and satisfies the condition

where C does not depend on and Then for is bounded from to and for is bounded from to
The following is a result of Adams-Guliyev type for the anisotropic Riesz potential.
Theorem 2. Let and let satisfies the conditions
and
where C does not depend on and Then the operator is bounded from
to for and from to
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