Weak type estimates for operators of potential type

• Autorzy: Richard L. Wheeden , Shiying Zhao
• Języki publikacji: EN

Abstrakty

EN

We derive two-weight weak type estimates for operators of potential type in homogeneous spaces. The conditions imposed on the weights are testing conditions of the kind first studied by E. T. Sawyer [4]. We also give some applications to strong type estimates as well as to operators on half-spaces.

Słowa kluczowe

EN

norm inequality; weight; operator of potential type; homogeneous space

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1996
• Tom: 119
• Numer: 2
• Strony: 149-160

Daty

wydano

1996

otrzymano

1995-04-20

poprawiono

1996-01-25

Twórcy

autor

Richard L. Wheeden

• Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.

autor

Shiying Zhao

• Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121, U.S.A.

Bibliografia

• [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
• [2] B. Franchi, C. E. Gutierrez and R. L. Wheeden, Weighted Sobolev-Poincaré inequalities for Grushin type operators, Comm. Partial Differential Equations 19 (1994), 523-604.
• [3] I. Genebashvili, A. Gogatishvili and V. Kokilashvili, Criteria of general weak type inequalities for integral transforms with positive kernels, Proc. Georgian Acad. Sci. Math. 1 (1993), 11-34.
• [4] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345.
• [5] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545.
• [6] E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874.
• [7] E. T. Sawyer, R. L. Wheeden and S. Zhao, Weighted norm inequalities for operators of potential type and fractional maximal functions, Potential Anal. (1996), to appear.
• [8] I. E. Verbitsky and R. L. Wheeden, Weighted norm inequalities for integral operators, to appear.