Joint weak type interpolation on Lorentz-Karamata spaces

Abstract

We present sharp interpolation theorems, including all limiting cases, for a class of quasilinear operators of joint weak type acting between Lorentz-Karamata spaces over $\sigma$-finite measure. This class contains many of the important integral operators. The optimality in the scale of Lorentz-Karamata spaces is also discussed. The proofs of our results rely on a characterization of Hardy-type inequalities restricted to monotone functions and with power-slowly varying weights. Some of the limiting cases of these inequalities have not been considered in the literature so far.

Preprint, 32 pages

Cited by in corpus (5)

• Lorentz--Karamata spaces
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• On Bilinear Hardy Inequality and Corresponding Geometric Mean Inequality
• On the smoothness of slowly varying functions
• Wiener-Luxemburg amalgam spaces