Related papers: On Polynomial Carleson operators along quadratic h…

Let $\L$ be a Schr\"odinger operator of the form $\L=-\Delta+V$ acting on $L^2(\mathbb R^n)$, $n\geq3$, where the nonnegative potential $V$ belongs to the reverse H\"older class $B_q$ for some $q\geq n.$ Let ${\rm BMO}_{{\mathcal{L}}}(\RR)$…

We proof pointwise bounds for rough Fourier integral operators by the $L^p$ Hardy-Littlewood maximal function. We assume the Fourier integral operators have amplitudes in $L^\infty S^m_\rho$ and phases $\varphi$ such that $\varphi(x,\xi) -…

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are…

Let $\mu$ be a non-negative Radon measure on ${\mathbb R}^d$ which only satisfies the polynomial growth condition. Let ${\mathcal Y}$ be a Banach space and $H^1(\mu)$ the Hardy space of Tolsa. In this paper, the authors prove that a linear…

We study maximal averages associated with singular measures on $\rr$. Our main result is a construction of singular Cantor-type measures supported on sets of Hausdorff dimension $1 - \epsilon$, $0 \leq \epsilon < {1/3}$ for which the…

We prove that for a finite type curve in $\mathbb R^3$ the maximal operator generated by dilations is bounded on $L^p$ for sufficiently large $p$. We also show the endpoint $L^p \to L^{p}_{1/p}$ regularity result for the averaging operators…

Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb…

We apply the Bennett-Carbery-Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved L^p estimates in the Stein restriction problem for dimension at least…

The bilinear maximal operator defined below maps $L^p\times L^q$ into $L^r$ provided $1<p,q<\zI$, $1/p+1/q=1/r$ and $2/3<r\le1$. $$ Mfg(x)=\sup_{t>0}\frac1{2t}\int_{-t}^t\abs{f(x+y)g(x-y)} dy.$$ In particular $Mfg$ is integrable\thinspace…

This work is concerned with extending the results of Calder\' on and Vaillancourt proving the boundedness of Weyl pseudo differential operators Op_h^{weyl} (F) in L^2(\R^n). We state conditions under which the norm of such operators has an…

This paper may be viewed as a companion paper to [G1]. In that paper, $L^2$ Sobolev estimates derived from a Newton polyhedron-based resolution of singularities method are combined with interpolation arguments to prove $L^p$ to $L^q_s$…

We extend the theorems of [G1] on $L^p$ to $L^p_s$ Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving $L^p$ to $L^q_s$ boundedness results for such operators. Here $q…

Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper,…

We consider the global Morrey-type spaces with variable exponents and general function defining these spaces. In the case of unbounded sets, we prove boundedness of the Hardy-Littlewood maximal operator, potential type operator in these…

Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\cal P}_{\leq N}$ denote the additive group of polynomials $P\in\mathbb{Z}[x]$ with ${\rm deg}\, P\leq N$ and $P(0)=0$. Given a unitary operator $U$…

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 that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the…

For a limited range of indices $p$, we obtain $L^p(\mathbb{R}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical H\"ormander smoothness estimate. These operators are assumed to be…

The article arXiv:1309.0945 by Do and Thiele develops a theory of Carleson embeddings in outer $L^p$ spaces for the wave packet transform of functions in $ L^p(\mathbb R)$, in the $2\leq p\leq \infty$ range referred to as local $L^2$. In…

A (d,k) set is a subset of R^d containing a translate of every k-dimensional plane. Bourgain showed that for 2^{k-1}+k \geq d, every (d,k) set has positive Lebesgue measure. We give an L^p bound for the corresponding maximal operator.