Double exponential integrability of convolution operators in generalized Lorentz-Zygmund spaces. (English) Zbl 0826.47021

This paper provides estimates for an appropriate norm of the convolution of a function in a Lorentz space with one in a generalized Lorentz- Zygmund space. As a corollary it is shown that the Riesz potential of a function in an appropriate generalized Lorentz-Zygmund space satisfies a ‘double exponential’ integrability condition. The results extend those of Brézis-Wainger on the convolution of functions in Lorentz spaces which lead to exponential integrability.
Reviewer: B.Opic (Praha)


47B38 Linear operators on function spaces (general)
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
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