Muckenhoupt-Wheeden conjectures in higher dimensions

• Autorzy: Alberto Criado , Fernando Soria
• Języki publikacji: EN

Abstrakty

EN

In recent work by Reguera and Thiele (2012) and by Reguera and Scurry (2013), two conjectures about joint weighted estimates for Calderón-Zygmund operators and the Hardy-Littlewood maximal function were refuted in the one-dimensional case. One of the key ingredients for these results is the construction of weights for which the value of the Hilbert transform is substantially bigger than that of the maximal function. In this work, we show that a similar construction is possible for classical Calderón-Zygmund operators in higher dimensions. This allows us to fully disprove the conjectures.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 1
• Strony: 25-45

Daty

wydano

2016

Twórcy

autor

Alberto Criado

• Departamento de Matemáticas, Facultad de Ciencia y Tecnología de la Universidad del País Vasco, 48080 Bilbao, Spain

autor

Fernando Soria

• Departamento de Matemáticas and Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/sm8357-3-2016