For the spherical mean operators $\scr {A} _t $ in $\Bbb {R}^ d $, $ d\ge 2$, we consider the
maximal functions $ M_Ef=\sup_ {t\in E}|\scr {A} _t f| $, with dilation sets $ E\subset [1, 2] $. In …

We prove a bilinear form sparse domination theorem that applies to many multi-scale
operators beyond Calderón–Zygmund theory, and also establish necessary conditions …

We derive sparse bounds for the bilinear spherical maximal function in any dimension d⩾ 1
d\geqslant1. When d⩾ 2 d\geqslant2, this immediately recovers the sharp L p× L q→ L r …

Let M be the maximal operator associated to a smooth curve in R 3 \documentclass[12pt]{minimal}
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} …

Given a hypersurface S⊂ R 2 d, we study the bilinear averaging operator that averages a
pair of functions over S, as well as more general bilinear multipliers of limited decay and …

We study L p× L q→ L r-boundedness of (sub) bilinear maximal functions associated with
degenerate hypersurfaces. First, we obtain the maximal bound on the sharp range of …

We prove estimates for local maximal operators associated with dilates of codimension two
spheres in Heisenberg groups; these are sharp up to two endpoints. The results can be …

In this paper, we study the L p (R 2)-improving bounds, ie, L p (R 2)→ L q (R 2) estimates, of
the maximal function M γ along a plane curve (t, γ (t)), where M γ f (x 1, x 2):= sup u∈[1, 2]∫ …

The Assouad dimension of the limit set of a geometrically finite Kleinian group with
parabolics may exceed the Hausdorff and box dimensions. The Assouad spectrum is a …

We study pointwise convergence of the fractional Schrödinger means along sequences tn
that converge to zero. Our main result is that bounds on the maximal function sup n| eitn …