Research Article
Year 2018,
Volume: 39 Issue: 2, 325 - 338, 29.06.2018
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.
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.
- [9]. Samko, S.G., Kilbas, A.A., and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Linghorne 1993.
- [10]. Sarikaya, M.Z., Yıldırım, H., The restriction and the continuity properties of potentials depending on λ-distance, Turk. J. Math., 30-3 (2006) 263-275.
- [11]. Sarikaya, M.Z., Yıldırım, H., On the β-spherical Riesz potential generated by the β-distance, Int. Journal of Contemp. Math. Sciences, 1, No. 1-4 (2006) 85-89.
- [12]. Sarikaya, M.Z., Yıldırım, H., On the non-isotropic fractional integrals generated by the λ-distance, Selçuk Journal of Appl. Math., 7-1 (2005) 17-23.
- [13]. Sarikaya, M.Z., Yıldırım, H., Ozkan, U. M., Norm inequalities with non-isotropic kernels, Int. Journal of Pure and Applied Mathematics, 31-3 (2006) 337-343.
- [14]. Schechter, M., Spectra of Partial Differential Operators. North Holland, 1986.
- [15]. Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Uni. Press, Princeton, New Jersey, 1970.
- [16]. Welland, G. V., Weighted norm inequalities for fractional integral. Proc. Amer. Math. Soc., 51 (1975) 143-148.
- [17]. Yıldırım, H., On generalization of the quasi homogeneous Riesz potential, Turk. J. Math., 29 (2005) 381-387.
Year 2018,
Volume: 39 Issue: 2, 325 - 338, 29.06.2018
Abstract
Bu
yazıda, [1] 'de tanımlanan potansiyel operatör için verilen eşitsizliğe benzer
β-mesafesi ile türetilen yeni ağırlıklı eşitsizlikler elde edilmiştir. Burada
sunulan sonuçlar daha önceki çalışmalarda ki verilenleri destekler.
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.
- [9]. Samko, S.G., Kilbas, A.A., and Marichev, O.I., Fractional Integrals and Derivatives, Theory and Applications, Gordon and Breach, Linghorne 1993.
- [10]. Sarikaya, M.Z., Yıldırım, H., The restriction and the continuity properties of potentials depending on λ-distance, Turk. J. Math., 30-3 (2006) 263-275.
- [11]. Sarikaya, M.Z., Yıldırım, H., On the β-spherical Riesz potential generated by the β-distance, Int. Journal of Contemp. Math. Sciences, 1, No. 1-4 (2006) 85-89.
- [12]. Sarikaya, M.Z., Yıldırım, H., On the non-isotropic fractional integrals generated by the λ-distance, Selçuk Journal of Appl. Math., 7-1 (2005) 17-23.
- [13]. Sarikaya, M.Z., Yıldırım, H., Ozkan, U. M., Norm inequalities with non-isotropic kernels, Int. Journal of Pure and Applied Mathematics, 31-3 (2006) 337-343.
- [14]. Schechter, M., Spectra of Partial Differential Operators. North Holland, 1986.
- [15]. Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Uni. Press, Princeton, New Jersey, 1970.
- [16]. Welland, G. V., Weighted norm inequalities for fractional integral. Proc. Amer. Math. Soc., 51 (1975) 143-148.
- [17]. Yıldırım, H., On generalization of the quasi homogeneous Riesz potential, Turk. J. Math., 29 (2005) 381-387.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 29, 2018 |
| Submission Date | September 1, 2017 |
| Acceptance Date | May 9, 2018 |
| Published in Issue | Year 2018Volume: 39 Issue: 2 |