Related papers: L^p regularity of averages over curves and bounds …

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First, we obtain an $H^1$ to $L^{1,\infty}$ bound for lacunary maximal operators under a dimensional assumption on the…

We study the boundedness problem for maximal operators $\mathbb{M}$ associated to averages along families of finite type curves in the plane, defined by $$\mathbb{M}f(x) \, := \, \sup_{1 \leq t \leq 2} \left|\int_{\mathbb{C}} f(x-ty) \,…

Let $M$ be the maximal operator associated to a smooth curve in $\mathbb R^3$ which has nonvanishing curvature and torsion. We prove that $M$ is bounded on $L^p$ if and only if $p>3$.

Extending the methods developed in the author's previous paper and using adapted coordinate systems in two variables, an L^p boundedness theorem is proven for maximal operators over hypersurfaces in R^3 when p > 2. When the best possible p…

In this paper, we study the $L^{p}$-improving property for the maximal operators along a large class of curves of finite type in the plane with dilation set $E \subset [1,2]$. The $L^{p}$-improving region depends on the order of finite type…

We investigate $L^p$ boundedness of the maximal function defined by the averaging operator $f\to \mathcal{A}_t^s f$ over the two-parameter family of tori $\mathbb{T}_t^{s}:=\{ ( (t+s\cos\theta)\cos\phi,\,(t+s\cos\theta)\sin\phi,\,…

We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities…

We study the boundedness problem for maximal operators $\mathcal{M}$ associated to averages along families of hypersurfaces $S$ of finite type in $\mathbb{R}^n.$ In this paper, we prove that if $S$ is a finite type hypersurface which is of…

We consider a type of maximal operators associated to moment curves in $\mathbb R^d, d\geq 3.$ We derive $L^p$ mapping properties for these operators. In a special case, the estimate is sharp.

We prove the $L^p$ boundedness of a maximal operator associated with a dyadic frequency decomposition of a Fourier multiplier, under a weak regularity assumption.

The aim of this article is to establish the $L^p(\mathbb{R}^2)$-boundedness of the variational operator associated with averaging operators defined over finite type curves in the plane. Additionally, we present the necessary conditions for…

For a function $f\in L^p(\Bbb R^d)$, $d\ge 2$, let $A_t f(x)$ be the mean of $f$ over the sphere of radius $t$ centered at $x$. Given a set $E\subset (0,\infty)$ of dilations we prove endpoint bounds for the maximal operator $M_E$ defined…

In this paper, we prove \( L^p \) boundedness results for lacunary elliptic maximal operators on the Heisenberg group. Furthermore, we extend these \( L^p \) estimates from skew-symmetric matrices, which naturally arise in Heisenberg group…

We prove $L^p$ bounds in the range $1<p<\infty$ for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof…

Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…

We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta <…

We prove a weighted inequality which controls conic Fourier multiplier operators in terms of lacunary directional maximal operators. By bounding the maximal operators, this enables us to conclude that the multiplier operators are bounded on…

We show that maximal operators formed by dilations of Mikhlin-H"ormander multipliers are typically not bounded on $L^p(R^d)$. We also give rather weak conditions in terms of the decay of such multipliers under which $L^p$ boundedness of the…

We study the $L^p$ mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this operator is bounded on $L^p$ for $p > 2$ in all dimensions $n…

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex…