analysis seminar

Event Type: 
Seminar
Speaker: 
Ramesh Manna, Harish-Chandra Research Institute
Event Date: 
Wednesday, February 24, 2016 -
3:00pm to 4:00pm
Location: 
smlc 356
Audience: 
General Public
Sponsor/s: 
M. Blair

Event Description: 

Title: Maximal averages associated with families of finite type surfaces

Abstract: In this talk, we will discuss the boundedness problem for
maximal operators M associated to averages along families of
hypersurfaces "S" of "finite type" in R^n. In the paper, we show that if
the surface S, is a finite type hypersurface which is of finite type k
at a_0, then the associated maximal operator is bounded on L^p(R^n) for
p>k. In this paper, we shall also consider a variable coefficient
version of maximal theorem and we obtain the same L^p- boundedness
result for p>k. In this talk, we will also discuss the consequence of
this result. In particular, we will discuss the connection between the
decay rate of the Fourier transform of the surface measure on S and the
L^p- boundedness of the associated maximal operator M.

References:
1) Ramesh Manna, Maximal averages associated to families of finite type
surfaces, arXiv 1510.08649.

2) Iosevich, A., Maximal operators associated to families of flat curves
in the plane, Duke Math. J., 76 (1994), no. 2 pp. 633-644.

3) Sogge, C. D., Maximal operators associated to hypersurfaces with one
nonvanishing principal curvature, Miraflores de la Sierra, Spain, 1992,
pp. 317-323,

Event Contact

Contact Name: M. Blair