On the exponential integrability of fractional integrals on spaces of homogeneous type

A. Gatto; Stephen Vági

Colloquium Mathematicae (1993)

  • Volume: 64, Issue: 1, page 121-127
  • ISSN: 0010-1354

Abstract

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In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds L 1 / α into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].

How to cite

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Gatto, A., and Vági, Stephen. "On the exponential integrability of fractional integrals on spaces of homogeneous type." Colloquium Mathematicae 64.1 (1993): 121-127. <http://eudml.org/doc/210161>.

@article{Gatto1993,
abstract = {In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds $L^\{1/α\}$ into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].},
author = {Gatto, A., Vági, Stephen},
journal = {Colloquium Mathematicae},
keywords = {normal space of homogeneous type; fractional integral},
language = {eng},
number = {1},
pages = {121-127},
title = {On the exponential integrability of fractional integrals on spaces of homogeneous type},
url = {http://eudml.org/doc/210161},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Gatto, A.
AU - Vági, Stephen
TI - On the exponential integrability of fractional integrals on spaces of homogeneous type
JO - Colloquium Mathematicae
PY - 1993
VL - 64
IS - 1
SP - 121
EP - 127
AB - In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds $L^{1/α}$ into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].
LA - eng
KW - normal space of homogeneous type; fractional integral
UR - http://eudml.org/doc/210161
ER -

References

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  1. [AB] D. R. Adams and R. J. Bagby, Translation-dilation invariant estimates for Riesz potentials, Indiana Univ. Math. J. 23 (1974), 1051-1067. Zbl0276.31003
  2. [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
  3. [GV] A. E. Gatto and S. Vági, Fractional integrals on spaces of homogeneous type, in: Analysis and Partial Differential Equations, C. Sadosky (ed.), Dekker, New York 1990, 171-216. 
  4. [H] L. I. Hedberg, On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505-510. Zbl0283.26003
  5. [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1964), 415-426. Zbl0102.04302
  6. [T] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-483. Zbl0163.36402
  7. [Z] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, Cambridge 1959. Zbl0085.05601

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