Abstract
A strong type two-weight problem is solved for fractional maximal functions defined in homogeneous type general spaces. A similar problem is also solved for one-sided fractional maximal functions.
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References
E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators.Studia Math. 75(1982), 1–11.
R. L. Wheeden, A characterization of some weighted norm inequalities for fractional maximal functions.Studia Math. 107(1993), 251–272.
M. Gabidzashvili, Weighted inequalities for anisotropic potentials. (Russian)Trudy Tbil. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR 89(1986), 25–36.
V. Kokilashvili and M. Gabidzashvili, Two-weight weak type inequalities for fractional type integrals.Preprint No. 45, Math. Inst. Czech. Akad. Sci., Praha, 1989.
J. O. Strömberg and A. Torchinsky, Weighted Hardy spaces.Lect. Notes in Math., v. 1381,Springer Verlag, New York, 1989.
I. Genebashvili, A. Gogatishvili, and V. Kokilashvili, Criteria of two-weghted inequalities for integral transforms with a positive kernel and maximal functions.Dokl. Akad. Nauk RAN (to appear).
I. Genebashvili, A. Gogatishvili, and V. Kokilashvili, Solution of two-weight problems for integral transforms with positive kernels.Georg. Math. J. 3(1996), 319–342.
A. Gogatishvili, and V. Kokilashvili, Criteria of weight inequalities for integral transforms defined on homogeneous type spaces. In: Topological Vector Spaces, Algebras and Related Areas.Longman. Pitman Research Notes in Mathematics 316(1994), 251–262.
B. Jawerth, Weighted inequalities for maximal operators: Linearization, localization and factorization.Amer. J. Math. 108(1986), 361–414.
R. L. Wheeden, Poincaré-Sobolev and isoperimetric inequalities, maximal functions and half-space estimates for the gradient. In: Nonlinear Analysis, Function Spaces and Applications, vol. 5, Proceedings.Prometheus Publishing House, 1994, 103–137.
E. T. Sawyer, R. L. Wheeden, and S. Zhao, Weighted norm inequalities for operators of potential type and fractional maximal functions.Potential Analysis (1995) (to appear).
F. J. Ruiz and J. L. Torrea, A unified approach to Carleson measures andA p weights, II.Pacific J. Math.,120(1985) 189–197.
I. Genebashvili, Generalized fractional maximal functions and potentials in weighted spaces.Proc. A. Razmadze Math. Inst. 102 (1993), 41–57.
F. J. Martin-Reyes and A. de la Torre, Two-weight norm inequalities for fractional one-sided maximal operators.Proc. Amer. Math. Soc. 117(1993), 483–499.
R. R. Coifman and G. Weiss, Analyse harmonique non-commutative sur certains espaces homogenes.Lecture Notes in Math. 242,Springer-Verlag, Berlin and New York, 1971.
R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in Analysis.Bull. Amer. Math. Soc. 83(1977), 569–645.
E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous type spaces.Amer. J. Math. 114(1992), 813–875.
R. L. Wheeden and S. Zhao, Weak type estimates for operators of potential type.Preprint. 1994.
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Gogatishvili, A., Kokilashvili, V. Criteria of strong type two-weighted inequalities for fractional maximal functions. Georgian Mathematical Journal 3, 423–446 (1996). https://doi.org/10.1007/BF02259772
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DOI: https://doi.org/10.1007/BF02259772