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Article

Keywords:
integral operator; anisotropic potential; weighted Lorentz space
Summary:
We give conditions on pairs of weights which are necessary and sufficient for the operator $T(f)=K\ast f$ to be a weak type mapping of one weighted Lorentz space in another one. The kernel $K$ is an anisotropic radial decreasing function.
References:
[1] Chang H.M., Hunt R.A., Kurtz D.S.: The Hardy-Littlewood maximal function on $L(p,q)$ spaces with weight. Indiana Univ. Math. J. 31 (1982), no.1, 109-120. MR 0642621
[2] Gabidzashvili M.: Weighted inequalities for anisotropic potentials. Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 25-36. MR 0884696
[3] Gabidzashvili M., Genebashvili J., Kokilashvili V.: Two weight inequalities for generalized potentials (in Russian). Trudy Mat. Inst. Steklov, to appear. MR 1221297
[4] Kokilashvili V.: Weighted inequalities for maximal functions and fractional integrals in Lorentz spaces. Math. Nachr. 133 (1987), 33-42. MR 0912418 | Zbl 0652.42005
[5] Kokilashvili V., Gabidzashvili M.: Weighted inequalities for anisotropic potentials and maximal functions (in Russian). Dokl. Akad. Nauk SSSR 282 (1985), no. 6, 1304-1306 English translation: Soviet Math. Dokl. 31 (1985), no. 3, 583-585. MR 0802694
[6] Kokilashvili V., Gabidzashvili M.: Two weight weak type inequalities for fractional type integrals. preprint no. 45, Mathematical Institute of the Czechoslovak Academy of Sciences, Prague 1989.
[7] Sawyer E.T.: A two weight type inequality for fractional integrals. Trans. Amer. Math. Soc. 281 (1984), no. 1, 339-345. MR 0719674
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