On molecules and fractional integrals on spaces of homogeneous type with finite measure

• Autorzy: A. Eduardo Gatto , Stephen Vági
• Języki publikacji: EN

Abstrakty

EN

In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the $H^p$ theory is given. Results are proved for $L^p$, $H^p$, BMO, and Lipschitz spaces.

Kategorie tematyczne

• 44A99: None of the above, but in this section
• 26A33: Fractional derivatives and integrals
• 42C99: None of the above, but in this section
• 31C15: Potentials and capacities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1992
• Tom: 103
• Numer: 1
• Strony: 25-39

Daty

wydano

1992

otrzymano

1990-11-08

poprawiono

1991-11-29

Twórcy

autor

A. Eduardo Gatto

• Department of Mathematics, DePaul University, Chicago, Illinois 60614, U.S.A.

autor

Stephen Vági

• Department of Mathematics, DePaul University, Chicago, Illinois 60614, U.S.A.

Bibliografia

• [CW] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
• [GV] A. E. Gatto and S. Vági, Fractional integrals on spaces of homogeneous type, in: Analysis and Partial Differential Equations, Cora Sadosky (ed.), Marcel Dekker, New York 1990, 171-216.
• [MS1] R. A. Macías and C. Segovia, Singular integrals on generalized Lipschitz and Hardy spaces, Studia Math. 65 (1979), 55-75.
• [MS2] R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type, Adv. in Math. 33 (1979), 271-309.
• [TW] M. H. Taibleson and G. Weiss, The molecular characterization of Hardy spaces, Astérisque 77 (1980), 66-149.