Weak -type estimates for singular integral and maximal operators
Abstract
In Chapter 3, the weak-type (1,1) constant for the Calderón-Zygmund singular integral operator T defined on L p([special characters omitted]) by [special characters omitted] is shown to be at worst c log n [special characters omitted]. In particular, for the jth-Riesz transform with [special characters omitted], the constant is at worst logarithmic with respect to dimension. In Chapter 4, it is shown that the weak-type inequality attains a limit as [special characters omitted]. In particular for [special characters omitted] with f ≥ 0,[special characters omitted] In Chapter 5, it is shown that the weak-type inequality attains a limit when f is replaced by certain singular measures on linear subspaces and [special characters omitted]. For example, if [special characters omitted] and [special characters omitted], is a singular measure in [special characters omitted], then [special characters omitted]
Degree
Ph.D.
Advisors
Banuelos, Purdue University.
Subject Area
Mathematics
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