# analysis seminar

### 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