Translation averages of dyadic weights are not always good weights.

Ward, Lesley A.. "Translation averages of dyadic weights are not always good weights.." Revista Matemática Iberoamericana 18.2 (2002): 377-407. <http://eudml.org/doc/39669>.

@article{Ward2002,
abstract = {The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights, and translation averages of dyadic reverse Holder weights need not be reverse Holder weights. All three results are proved using the same construction.},
author = {Ward, Lesley A.},
journal = {Revista Matemática Iberoamericana},
keywords = {Funciones de oscilación media acotada; Espacios de funciones; Operadores maximales; Funciones de peso; Análisis de Fourier; doubling measures; dyadic reverse Hölder weights; dyadic weights; dyadic Muckenhoupt weights},
language = {eng},
number = {2},
pages = {377-407},
title = {Translation averages of dyadic weights are not always good weights.},
url = {http://eudml.org/doc/39669},
volume = {18},
year = {2002},
}

TY - JOUR
AU - Ward, Lesley A.
TI - Translation averages of dyadic weights are not always good weights.
JO - Revista Matemática Iberoamericana
PY - 2002
VL - 18
IS - 2
SP - 377
EP - 407
AB - The process of translation averaging is known to improve dyadic BMO to the space BMO of functions of bounded mean oscillation, in the sense that the translation average of a family of dyadic BMO functions is necessarily a BMO function. The present work investigates the effect of translation averaging in other dyadic settings. We show that translation averages of dyadic doubling measures need not be doubling measures, translation averages of dyadic Muckenhoupt weights need not be Muckenhoupt weights, and translation averages of dyadic reverse Holder weights need not be reverse Holder weights. All three results are proved using the same construction.
LA - eng
KW - Funciones de oscilación media acotada; Espacios de funciones; Operadores maximales; Funciones de peso; Análisis de Fourier; doubling measures; dyadic reverse Hölder weights; dyadic weights; dyadic Muckenhoupt weights
UR - http://eudml.org/doc/39669
ER -