Strong $A_\infty$-weights are $A_\infty$-weights on metric spaces

On non-effective weights in Orlicz spaces

Given a weight in , and a Young function , we consider the weighted modular ( ( )) ( ) and the resulting weighted Orlicz space ( ). For a Young function ∆ ( ) we present a necessary and sufficient conditions in order that ( ) = ( ) up to the equivalence of norms. We find a necessary and sufficient condition for in order that there exists an unbounded weight such that the above equality of space...

Bilipschitz Mappings and Strong a 1 Weights

Given a doubling measure on R n , one can deene an associated quasidistance on R n by (x; y) = (B x;y) 1=n ; where B x;y is the smallest ball which contains the points x and y. This paper is concerned with the resulting geometry which is induced by. The main result provides a condition on under which R n equipped with the quasidistance (;) admits a bilipschitz embedding into R N with the standa...

Modulation Spaces with A loc ∞ - Weights

On strong 1-factors and Hamilton weights of cubic graphs

A 1-factor M of a cubic graph G is strong if |M ∩ T |= 1 for each 3-edge-cut T of G. It is proved in this paper that a cubic graph G has precisely three strong 1-factors if and only if the graph can be obtained from K4 via a series of 4 ↔ Y operations. Consequently, the graph G admits a Hamilton weight and is uniquely edge-3-colorable. c © 2001 Elsevier Science B.V. All rights reserved.

Boundedness of the Riesz Projection on Spaces with Weights

Let ∂D be the unit circle in the complex plane, define the function χ on ∂D by χ(eiθ) = eiθ, and set P = {p : p = ∑Nk=−N ckχ}. Let σ be normalized Lebesgue measure on ∂D. The Riesz projection P+ is defined on P by the formula P+( ∑N k=−N ckχ k) = ∑N k=0 ckχ k. In [4], Paul Koosis proved: Theorem 1 (Koosis). Given a non-negative function w ∈ L1, there exists a non-negative, non-trivial function ...