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

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

Abstrakty

EN

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].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 64
• Numer: 1
• Strony: 121-127

Daty

wydano

1993

otrzymano

1991-01-25

poprawiono

1992-01-20

Twórcy

autor

A. Eduardo Gatto

• Department of Mathematical Sciences, DePaul University, 2219 North Kenmore Ave., Chicago, Illinois 60614, U.S.A.

autor

Stephen Vági

• Department of Mathematical Sciences, DePaul University, 2219 North Kenmore Ave., Chicago, Illinois 60614, U.S.A.

Bibliografia

• [AB] D. R. Adams and R. J. Bagby, Translation-dilation invariant estimates for Riesz potentials, Indiana Univ. Math. J. 23 (1974), 1051-1067.
• [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, C. Sadosky (ed.), Dekker, New York 1990, 171-216.
• [H] L. I. Hedberg, On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505-510.
• [JN] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1964), 415-426.
• [T] N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-483.
• [Z] A. Zygmund, Trigonometric Series, 2nd ed., Cambridge Univ. Press, Cambridge 1959.