Elementary reverse Hölder type inequalities with application to operator interpolation theory

Bastero, Jesús; Ruiz, Francisco

doi:10.1090/S0002-9939-96-03651-9

Elementary reverse Hölder type inequalities with application to operator interpolation theory
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by Jesús Bastero and Francisco J. Ruiz PDF

Proc. Amer. Math. Soc. 124 (1996), 3183-3192 Request permission

Abstract:

We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on $L^{p}$ of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.

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