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Mapping Properties of Certain Averaging Operators


Erdoğan, Mehmet Burak (2002) Mapping Properties of Certain Averaging Operators. Dissertation (Ph.D.), California Institute of Technology.


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.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Makarov, Nikolai G.
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 July 2001
Record Number:CaltechTHESIS:01242012-162804546
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6773
Deposited By: Benjamin Perez
Deposited On:25 Jan 2012 15:38
Last Modified:10 Feb 2017 22:33

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