Related papers: An estimate for narrow operators on $L^p([0, 1])$

Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, $L^2$ whenever $v$ is Lipschitz. We establish a wide range of $L^p$ estimates for this operator when $v$ is a measurable, non-vanishing,…

We prove $L^p$ and smoothing estimates for the resolvent of magnetic Schr\"odinger operators. We allow electromagnetic potentials that are small perturbations of a smooth, but possibly unbounded background potential. As an application, we…

In this paper we prove a version of the Gohberg lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators on compact Lie groups. As a consequence, we prove several…

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…

We obtain Fourier inequalities in the weighted $L_p$ spaces for any $1<p<\infty$ involving the Hardy-Ces\`aro and Hardy-Bellman operators. We extend these results to product Hardy spaces for $p\le 1$. Moreover, boundedness of the…

\begin{abstract} Let $P\pm$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider estimates of the expression $\|( |P_ + f | ^s + |P_- f |^s) ^{\frac{1}{s}}\|_{L^p (\mathbf{T})}$ in terms of Lebesgue $p$-norm of the…

We prove a generalization of a Hardy type inequality for negative exponents valid for non-negative functions defined on $(0,1]$. As an application we find the exact best possible range of $p$ such that $1<p\le q$ such that any…

We provide an example of a pair of weights $(u,v)$ for which the Hardy-Littlewood maximal function is bounded from $L^p(v)$ to $L^p(u)$ and from $L^{p'}(u^{1-p'})$ to $L^{p'}(v^{1-p'})$ while a dyadic sparse operator is not bounded on the…

In this paper, we study the persistence approximation property for quantitative $K$-theory of filtered $L^p$ operator algebras. Moreover, we define quantitative assembly maps for $L^p$ operator algebras when $p\in [1,\infty)$. Finally, in…

We prove two theorems about convolution operators on $L^p(G)$ for a locally compact group $G$. First, if $G$ has the approximation property, then the algebra of convoluters is the algebra of pseudo-measures. Second, the bicommutant of the…

We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $\R^N$ belongs to trace classes $\cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of…

Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le\infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show…

For $1<p<\infty$ and $M$ the centered Hardy-Littlewood maximal operator on $\mathbb{R}$, we consider whether there is some $\varepsilon=\varepsilon(p)>0$ such that $\|Mf\|_p\ge (1+\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\le…

Results concerning set theoretic continuity properties of the spectrum of the Harper operator are extended to a large class (generalized Harper operators (GHO)) of operators in $L^{2}(\bZ^{2})$.

We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. (4) 88: 229-305, 1971) shows that if the operator has…

In this paper we investigate a class of domains $\Omega^{n+1}_k =\{(z,w)\in \mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$ which generalizes the Hartogs triangle. we first obtain the new explicit formulas for the…

Let $D$ be a strictly pseudoconvex domain in $\C^N$ and $X$ a pure-dimensional non-reduced subvariety that behaves well at $\partial D$. We provide $L^p$-estimates of extensions of holomorphic functions defined on $X$.

The main result of this paper is the existence of a hyperinvariant subspace of weighted composition operator $Tf=vf\circ\tau$ on $L^p([0,1]^d)$, ($1 \leq p \leq \infty$) when the weight $v$ is in the class of ``generalized polynomials'' and…

In this paper, we consider the $L_x^p(\mathbb{R}^2)\rightarrow L_{x,u}^q(\mathbb{R}^2\times [1,2])$ estimate for the operator $T$ along a dilated plane curve $(ut,u\gamma(t))$, where $$Tf(x,u):=\int_{0}^{1}f(x_1-ut,x_2-u…

The norm of $C-I$ on $\ell^p$, where $C$ is the Ces\`aro operator, is shown to be $1/(p-1)$ when $1<p\le2$. This verifies a recent conjecture of G. J. O. Jameson. The norm of $C-I$ on $\ell^p$ is also determined when $2< p<\infty$. The two…