Criteria of Strong Type Two-Weighted Inequalities for Fractional Maximal Functions

Georgian Mathematical Journal

Volumn 3, Issue 5, 1996, Pages 423-446

  Gogatishvili, A ^a   Kokilashvili, V ^a  

^a A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

Author keywords

Fractional maximal function; Homogeneous type space; One sided fractional maximal functions; Strong type two weighted inequality

Indexed keywords

EID: 35648996063     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.1996.423     Document Type: Article

References (18)

1. E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators. Studia Math. 75(1982), 1-11.
2. R. L. Wheeden, A characterization of some weighted norm inequalities for fractional maximal functions. Studia Math. 107(1993), 251-272.
3. M. Gabidzashvili, Weighted inequalities for anisotropic potentials. (Russian) Trudy Tbil. Mat. Inst. Razmadze Akad. Nauk Gruz. SSR 89(1986), 25-36.
4. V. Kokilashvili and M. Gabidzashvili, Two-weight weak type inequalities for fractional type integrals. Preprint No. 45, Math. Inst. Czech. Akad. Sci., Praha, 1989.
5. J. O. Strömberg and A. Torchinsky, Weighted Hardy spaces. Led. Notes in Math., v. 1381, Springer Verlag, New York, 1989.
6. I. Genebashvili, A. Gogatishvili, and V. Kokilashvili, Criteria of twoweghted inequalities for integral transforms with a positive kernel and maximal functions. Dokl. Akad. Nauk RAN (to appear).
7. I. Genebashvili, A. Gogatishvili, and V. Kokilashvili, Solution of two-weight problems for integral transforms with positive kernels. Georg. Math. J. 3(1996), 319-347.
8. 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.
9. B. Jawerth, Weighted inequalities for maximal operators: Linearization, localization and factorization. Amer. J. Math. 108(1986), 361-414.
10. 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.
11. 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).
12. F. J. Ruiz and J. L. Torrea, A unified approach to Carleson measures and Ap weights, II. Pacific J. Math. 120(1985) 189-197.
13. I. Genebashvili, Generalized fractional maximal functions and potentials in weighted spaces. Proc. A. Razmadze Math. Inst. 102(1993), 41-57.
14. E. J. Martin-Reyes and de la Torre, Two-weight norm inequalities for fractional one-sided maximal operators. Proc. Amer. Math. Soc. 117(1993), 483-499.
15. 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.
16. R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in Analysis. Bull. Amer. Math. Soc. 83(1977), 569-645.
17. 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.
18. R. L. Wheeden and S. Zhao, Weak type estimates for operators of potential type. Preprint. 1994.