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ArticleOriginal scientific text

Title

Mapping properties of integral averaging operators

Authors 1, 2

Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
  2. Department of Mathematics, University of Western Ontario, London, Ontario, N6A 5B7, Canada

Abstract

Characterizations are obtained for those pairs of weight functions u and v for which the operators Tf(x)=ʃa(x)b(x)f(t)dt with a and b certain non-negative functions are bounded from Lp_u(0,∞) to Lq_v(0,∞), 0 < p,q < ∞, p≥ 1. Sufficient conditions are given for T to be bounded on the cones of monotone functions. The results are applied to give a weighted inequality comparing differences and derivatives as well as a weight characterization for the Steklov operator.

Keywords

ENG
integral averaging operator, weight characterizations, Hardy inequalities, Steklov operator, differences

Bibliography

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Studia Mathematica
1998/129/2
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Pages:
157-177
Main language of publication
English
Received
1997-04-15
Accepted
1997-10-13
Published
1998
Exact and natural sciences