Linear and sublinear operators acting from the scale of spaces to a certain fixed quasinormed space are considered. It is shown how the extrapolation construction proposed by Jawerth and Milman at the end of 1980s can be used to extend a bounded action of an operator from the scale to wider spaces. Theorems are proved which generalize Yano's extrapolation theorem to the case of a quasinormed target space. More precise results are obtained under additional conditions on the quasinorm. Bibliography: 35 titles.

Extrapolation of operators acting into quasi-Banach spaces

We show that the extremal extrapolation spaces for an operator with any function ξ characterizing the growth of the operator norms are the sum and the intersection of spaces whose norms depend on ξ and are written out explicitly.

Extremal Extrapolation Spaces

We show that the calculation of the sum of local Morrey spaces can be reduced to the calculation of the sum of sequence spaces that appear as parameters in the definition of local Morrey spaces. The presence of such a reduction allows us to obtain new extrapolation theorems for local Morrey spaces with sharp constants.

Sharp Extrapolation Theorems for Local Morrey Spaces

The calculation of the sum of the spaces of the K‐method of real interpolation

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Экстраполяция операторов, действующих в квазибанаховы пространства@@@Extrapolation of operators acting into quasi-Banach spaces

It is shown that an extrapolation theorem for Lp proposed by the author and a Yanotype theorem implied by it cannot be improved.

Can Yano’s extrapolation theorem be strengthened?

A method for exactly calculating norm on the sum of the cones of nonincreasing or concave functions in Lorentz spaces is proposed. The obtained result makes it possible to prove new extrapolation theorems for cones in Lorentz, Lebesgue, and Marcinkiewicz spaces with exact constants.

E. I. Berezhnoi

Papers

Can Yano’s extrapolation theorem be strengthened?

Exact Calculation of Sums of Cones in Lorentz Spaces

Extremal Extrapolation Spaces