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

A. Gatto; Stephen Vági

Studia Mathematica (1992)

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

Abstract

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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.

How to cite

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Gatto, 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

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  1. [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
  2. [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. 
  3. [MS1] R. A. Macías and C. Segovia, Singular integrals on generalized Lipschitz and Hardy spaces, Studia Math. 65 (1979), 55-75. Zbl0479.42014
  4. [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
  5. [TW] M. H. Taibleson and G. Weiss, The molecular characterization of Hardy spaces, Astérisque 77 (1980), 66-149. 

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