Erdoğan, Mehmet Burak (2002) Mapping properties of certain averaging operators. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:01242012-162804546
In this thesis, we investigate the mapping properties of two averaging operators.
In the first part, we consider a model rigid well-curved line complex G_d in R^d. The X-ray transform, X, restricted to G_d is defined as an operator from functions on R^d to functions on G_d in the following way: Xf(l) = ∫_lf, l ϵ G_d. We obtain sharp mixed norm estimates for X in R^4 and R^5.
In the second part, we consider the elliptic maximal function M. Let ε be the set of all ellipses in R^2 centered at the origin with axial lengths in [1/2,2]. Let f : R^2 -> R, then M f : R^2 -> R is defined in the following way: Mf(x) = ^(sup)_(Eϵε) ^1/_(|E|) ∫_E f(x+s)dσ(s), where dσ is the arclength measure on E and |E| is the length of E.
In this part of the thesis, we investigate the L^P mapping properties of M.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Restricted to Caltech community only|
|Defense Date:||23 July 2001|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Benjamin Perez|
|Deposited On:||25 Jan 2012 15:38|
|Last Modified:||26 Dec 2012 04:39|
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