On Hardy type inequality with non-isotropic kernels
Lobachevskii journal of mathematics, Tome 22 (2006), pp. 47-57.

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In the present paper we establish a Stein–Weiss type generalization of the Hardy type inequality with non-isotropic kernels depending on $\lambda$-distance for the spaces $L_{p(.)}(\Omega)$ with variable exponent $p(x)$ in the case of bounded domains $\Omega$ in $R^n$.
Keywords: Riesz potential, Hardy inequality, maximal function.
Mots-clés : non-isotropic distance
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M. Z. Sarikaya; H. Yildirim. On Hardy type inequality with non-isotropic kernels. Lobachevskii journal of mathematics, Tome 22 (2006), pp. 47-57. http://geodesic.mathdoc.fr/item/LJM_2006_22_a5/

[1] Besov, O. V. and Lizorkin, P. I., “The $L^p$ estimates of a certain class of non-isotropic singular integrals”, Dokl. Akad. Nauk SSSR, 69 (1960), 1250–1253 | MR

[2] Diening, L., “Maximal function on generalized Lebesgue spaces”, Math. Ineq. and Appl., 7:2 (2004), 245–253 | MR | Zbl

[3] Hardy, H. G. and Littlewood, J. E, “Some properties of fractional integrals, I”, Math. Z., 27:4 (1928), 565–606 | DOI | MR | Zbl

[4] Kokilashvili, V. and Samko, S., “Maximal and fractional operators in weighted $L_{p(x)}$ spaces”, Rev. Mat. Iberoam., 20:2 (2004), 493–515 | MR | Zbl

[5] Muckenhoupt, B., “Weighted norm inequalities for the Hardy maximal function”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[6] Samko, S., “Hardy inequality in the generalized Lebesgue spaces”, Fract. Calc and Appl. Anal., 6:4 (2003), 355–362 | MR | Zbl

[7] Sarikaya, M. Z. and Yıldırım, H., “The Restriction and the Continuity Properties of Potentials Depending On $\lambda$-Distance”, Turkish J. Math., 30:3 (2006), 263–275 | MR | Zbl

[8] Sarikaya, M. Z. and Yıldırım, H., “On the $\beta$-spherical Riesz potential generated by the $\beta$-distance”, Int. Journal of Contemp. Math. Sciences, 1:1–4 (2006), 85–89 | MR | Zbl

[9] Sarikaya, M. Z. and Yıldırım, H., “On the non-isotropic fractional integrals generated by the $\lambda$-distance”, Selçuk J. Appl. Math., 7:1 (2006), 17–23 | MR | Zbl

[10] Stein, E. M., Singular integrals differential properties of functions, Princeton Uni. Press, Princeton, New Jersey, 1970 | MR

[11] Yıldırım, H., “On Generalization of The Quasi Homogeneous Riesz Potential”, Turk. J. Math., 29:4 (2005), 381–387 | MR