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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. doi:10.7907/JRFS-4S52.


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):
  • Wolff, Thomas H. (advisor)
  • Ramakrishnan, Dinakar
Thesis Committee:
  • Makarov, Nikolai G. (chair)
  • Hundertmark, Dirk
  • Simon, Barry M.
  • Wales, David B.
  • Wolff, Thomas H.
  • Ramakrishnan, Dinakar
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:05 Nov 2021 20:25

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