The Marcinkiewicz interpolation theorem

An Extension of the Marcinkiewicz Interpolation Theorem to Lorentz Spaces

V J o v J t f(y) ) " ) 7 V J o ~ ) • Third, previously open questions concerning the Marcinkiewicz Theorem are settled by showing our result is best possible. Consider complex-valued, measurable functions ƒ defined on a measure space (ikf, m). The distribution function of ƒ is defined by (2) X(y) = X/GO =m{xeM:\ ƒ(*) | > y}, y > 0. X(y) is nonincreasing and continuous from the right. The noninc...

An Essay on the Interpolation Theorem of Józef Marcinkiewicz - Polish Patriot

Real Interpolation for Non - Distant Marcinkiewicz Spaces ∗

We describe the real interpolation spaces between given Marcinkiewicz spaces that have fundamental functions of the form t ( ln et )α with the same exponent q. The spaces thus obtained are used for the proof of optimal interpolation theorem from [7], concerning spaces L∞,α,E .

On a Theorem of Marcinkiewicz and Zygmund

The purpose of the present paper is to prove the following result: Let F(P), P= (xi, x2, • ■ • , x„), be a function harmonic for xn >0 and such that for every point Q of a set £ of positive measure on the hyperplane x„ = 0 there exists a region contained in x„>0 limited by a cone with vertex at Q and a hyperplane x„ = const, where the function is bounded. Then except for a set of measure Zero, ...

An interpolation theorem

Lyndon's Interpolation Theorem asserts that for any valid implication between two purely relational sentences of rst-order logic, there is an interpolant in which each relation symbol appears only in those polarities in which it appears in both the antecedent and the succedent of the given implication. This note proves a similar interpolation result under the additional requirement that, for so...