Sharp weighted estimates for singular integral operators

Singular integrals;A p weights;Calderon-Zygmund operators;Muckenhoupt-Wheeden conjecture;A 2 conjecture;Sharp estimates

Reguera Rodriguez, Maria del Carmen ; Mathematics

University:Georgia Institute of Technology

Department:Mathematics

关键词: Singular integrals;    A p weights;    Calderon-Zygmund operators;    Muckenhoupt-Wheeden conjecture;    A 2 conjecture;    Sharp estimates;   

Others  :  https://smartech.gatech.edu/bitstream/1853/39522/1/reguerarodriguez_mariadelcarmen_201105_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

The thesis provides answers, in one case partial and in the other final, to two conjectures in the area of weighted inequalities for Singular Integral Operators. We study the mapping properties of these operators in weighted Lebesgue spaces with weight w. The novelty of this thesis resides in proving sharp dependence of the operator norm on the Muckenhoupt constant associated to the weigth w for a rich class of Singular Integral operators. The thesis also addresses the end point case p=1, providing counterexamples for the dyadic and continuous settings.