Maximal functions and Hilbert transforms associated to polynomials

Surface Measures - Maximal Functions and Fourier Transforms

Maximal Functions Associated to Filtrations

Let T be a bounded linear, or sublinear, operator from L p (Y) to L q (X). To any sequence of subsets Y j of Y is associated a maximal operator T f(x) = sup j jT (f Yj)(x)j. Under the hypotheses that q > p and the sets Y j are nested, we prove that T is also bounded. Classical theorems of Menshov and Zygmund are obtained as corollaries. Multilinear generalizations of this theorem are also estab...

Line graphs associated to the maximal graph

Let $R$ be a commutative ring with identity. Let $G(R)$ denote the maximal graph associated to $R$, i.e., $G(R)$ is a graph with vertices as the elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $R$ containing both. Let $Gamma(R)$ denote the restriction of $G(R)$ to non-unit elements of $R$. In this paper we study the various graphi...

Singular Radon Transforms and Maximal Functions under Convexity Assumptions

We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane.

L estimates for angular maximal functions associated with Stieltjes and Laplace transforms

Maximal angular operator sends a function defined in a sector of the complex plane to a function of modulus obtained by maximizing over all admissible values of the argument for the given modulus. The compositions of the so obtained maximal angular operator with the Poisson, Stieltjes and Laplace transform (in the sectors of their respective ranges) are shown to be bounded (nonlinear) operators...