20,416 research outputs found
Exponential sums and polynomial congruences in two variables: the quasi-homogeneous case
We adapt ideas of Phong, Stein and Sturm and ideas of Ikromov and M\"uller
from the continuous setting to various discrete settings, obtaining sharp
bounds for exponential sums and the number of solutions to polynomial
congruences for general quasi-homogeneous polynomials in two variables. This
extends work of Denef and Sperber and also Cluckers regarding a conjecture of
Igusa in the two dimensional setting by no longer requiring the polynomial to
be nondegenerate with respect to its Newton diagram
Optical surface pressure measurement using pressure sensitive paint
SIGLEAvailable from British Library Document Supply Centre-DSC:DXN034175 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Problems on averages and lacunary maximal functions
We prove three results concerning convolution operators and lacunary maximal
functions associated to dilates of measures. First, we obtain an to
bound for lacunary maximal operators under a dimensional
assumption on the underlying measure and an assumption on an regularity
bound for some . Secondly, we obtain a necessary and sufficient condition
for boundedness of lacunary maximal operator associated to averages over
convex curves in the plane. Finally we prove an regularity result for
such averages. We formulate various open problems.Comment: To appear in the Marcinkiewicz Centenary Volume (Banach Center
Publications 95
- …