IJPAM: Volume 52, No. 3 (2009)

ON THE RIESZ DIAMOND POTENTIAL
AND ITS INVERSION PROBLEM

Rubén Alejandro Cerutti
Facultad de Ciencias Exactas y Naturales y Agrimensura
Universidad Nacional del Nordeste
Avda. Libertad, 5540 (3400) Corrientes, ARGENTINA
e-mail: [email protected]


Abstract.By the convolution of an adecuate function $f$ with the Diamond Riesz kernel the Riesz Diamond potential of order $\left(\alpha,\beta\right)$ is introduced. We study some elementary properties and the inversion problem is solved by using hypersingular integral operators defining certain fractional derivative as the inverse operator.

Received: March 12, 2009

AMS Subject Classification: 46F10

Key Words and Phrases: Riesz potential, Riesz Diamond kernel, hypersingular integrals

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 3