EN
TR
Non-Isotropic Potential Theoretic Inequality
Abstract
In this paper, the new weighted inequalities were derived by β-distance which is similar to the given inequality for the potential operator defined in [1]. The results presented here would provide extensions of those given in earlier works.
Keywords
References
- [1]. Adams, D., Traces of potentials arising from traslation invariant operators, Ann. Scuola Norm. Sup. Pisa, 25 (1971) 203-217.
- [2]. Besov, O.V., Lizorkin, P.I., The L^{p} estimates of a certain class of non-isotropic singular integrals, Dokl. Akad. Nauk, SSSR, 69 (1960) 1250-1253.
- [3]. Garcia-Cuerva, J., Martell, J.M., Two-weight norm inequalies for maximal operator and fractional integrals on non-homogeneous spaces, Indiana Univ. Math. J., 50-3 (2001) 1241-1280.
- [4]. Hedberg, L., On certain convolution inequalities. Proc. Amer. Math. Soc. 36 (1972) 505-510.
- [5]. Kufner, A., O. John and S. Fucik, Function spaces, Academia, Prague and Noordhoff, Leyden 1977.
- [6]. Levitan, B.M., Generelized Translation Operators and Some of Their Applications, Nauka, Moscow, 1962; English translation: Israel Program for Scientific Translation 1964.
- [7]. Morrey, C.B., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938) 126-166.
- [8]. Ragusa, M. A., Catania, and P. Zamboni, Sant'agata-Messina, A Potential Theoretic Inequality, Czechoslovak Mathematical Journal, 51-126 (2001) 55-65.
Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
June 29, 2018
Submission Date
September 1, 2017
Acceptance Date
May 9, 2018
Published in Issue
Year 2018 Volume: 39 Number: 2