On a Sobolev Type Theorem for the Generalized Riesz Potential Generated by the Generalized Shift Operator on Morrey Space
DOI:
https://doi.org/10.5644/SJM.04.2.06Keywords:
Riesz potential, shift operator, Morrey spaceAbstract
In this paper, we give a generalized definition of Morrey space for Lebesgue measure. In this space, the inequality of Hardy-Sobolev type is established for the generalized Riesz potentials generated by the generalized shift operator.
2000 Mathematics Subject Classification. 31B10, 44A15
Downloads
References
F. Chiarenza and M. Frasca, Morrey spaces and Hardy-Littlewood Maximal Function, Rend. Mat. Appl., 7 (3-4) (1987), 271–279.
B. M. Levitan, B.M., Expansion in Fourier Series and Integrals with Bessel Functions, Uspehi Mat. Nauk (N.S), 6 no. 2(42) (1951), 102–143 (in Russian).
B. M. Levitan, Generelized Translation Operators and Some of Their Applications, Moscova 1962 (Translation 1964).
C. B. Morrey, On the solutions of quasi-linear elliptic partial differential equations, Trans.Amer. Math. Soc., 43 (1938), 126–166.
E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr., 166 (1994), 95–103.
S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives, Theory and Application, Gordan and Breach Science USA 1993.
E. M. Stein, Singular Integrals and Differential Properties of Functions, Princeton University Press, Princeton, New Jersey, (1970).
H. Yıldırım, Riesz Potentials Generated by a Generalized Shift Operator, Ph.D. Thesis 1995.
