A Multilinear Version of 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...

Some Remarks on Multilinear Maps and Interpolation

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including estimates for bilinear fractional integrals.

A More General Version of the Costa Theorem

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

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

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, ...