Citation
Erdoğan, Mehmet Burak (2002) Mapping properties of certain averaging operators. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:01242012162804546
Abstract
In this thesis, we investigate the mapping properties of two averaging operators.
In the first part, we consider a model rigid wellcurved line complex G_d in R^d. The Xray 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.)) 

Subject Keywords:  Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  23 July 2001 
Record Number:  CaltechTHESIS:01242012162804546 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:01242012162804546 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6773 
Collection:  CaltechTHESIS 
Deposited By:  Benjamin Perez 
Deposited On:  25 Jan 2012 15:38 
Last Modified:  26 Dec 2012 04:39 
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