A characterization of some weighted norm inequalities for the fractional maximal function

• Autorzy: Richard L. Wheeden
• Języki publikacji: EN

Abstrakty

EN

A new characterization is given for the pairs of weight functions v, w for which the fractional maximal function is a bounded operator from $L^p_v(X)$ to $L_w^q(X)$ when 1 < p < q < ∞ and X is a homogeneous space with a group structure. The case when X is n-dimensional Euclidean space is included.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 107
• Numer: 3
• Strony: 257-272

Daty

wydano

1993

otrzymano

1992-01-02

poprawiono

1993-04-20

Twórcy

autor

Richard L. Wheeden

• Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903-2101, U.S.A.

Bibliografia

• [FS] C. L. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
• [GK] M. Gabidzashvili and V. Kokilashvili, Two weight weak type inequalities for fractional-type integrals, preprint, No. 45, Math. Inst. Czech. Acad. Sci., Prague, 1989.
• [P] C. Perez, Two weighted norm inequalities for Riesz potentials and uniform $L^p$-weighted Sobolev inequalities, Indiana Univ. Math. J., 39 (1990), 31-44.
• [S1] E. T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), 1-11.
• [S2] E. T. Sawyer, A two weight weak type inequality for fractional integrals, Trans. Amer. Math. Soc. 281 (1984), 339-345.
• [S3] E. T. Sawyer, A characterization of two weight norm inequalities for fractional and Poisson integrals, ibid. 308 (1988), 533-545.
• [SW1] E. T. Sawyer and R. L. Wheeden, Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces, Amer. J. Math. 114 (1992), 813-874.
• [SW2] E. T. Sawyer and R. L. Wheeden, Carleson conditions for the Poisson integral, Indiana Univ. Math. J. 40 (1991), 639-676.