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

Studia Mathematica (1992)

- Volume: 103, Issue: 1, page 25-39
- ISSN: 0039-3223

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topGatto, A., and Vági, Stephen. "On molecules and fractional integrals on spaces of homogeneous type with finite measure." Studia Mathematica 103.1 (1992): 25-39. <http://eudml.org/doc/215933>.

@article{Gatto1992,

abstract = {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.},

author = {Gatto, A., Vági, Stephen},

journal = {Studia Mathematica},

keywords = {functions of bounded mean oscillation; continuity; fractional integrals; spaces of homogeneous type; molecules; BMO; Lipschitz spaces},

language = {eng},

number = {1},

pages = {25-39},

title = {On molecules and fractional integrals on spaces of homogeneous type with finite measure},

url = {http://eudml.org/doc/215933},

volume = {103},

year = {1992},

}

TY - JOUR

AU - Gatto, A.

AU - Vági, Stephen

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

JO - Studia Mathematica

PY - 1992

VL - 103

IS - 1

SP - 25

EP - 39

AB - 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.

LA - eng

KW - functions of bounded mean oscillation; continuity; fractional integrals; spaces of homogeneous type; molecules; BMO; Lipschitz spaces

UR - http://eudml.org/doc/215933

ER -

## References

top- [CW] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645. Zbl0358.30023
- [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. Zbl0479.42014
- [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. Zbl0431.46019
- [TW] M. H. Taibleson and G. Weiss, The molecular characterization of Hardy spaces, Astérisque 77 (1980), 66-149.

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