Related papers: New estimates for the Beurling-Ahlfors operator on…

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable…

We extend the so-called universal potential estimates of the Kuusi-Mingione type (J.Funct. Anal. 2012) to the singular case $1<p\leq 2-1/n$ for the quasilinear equation with measure data \begin{equation*} -\operatorname{div}(A(x,\nabla…

We establish the $L^p$-boundedness of the local covariant Riesz transform for differential forms on manifold $M$ with bounded $\|Rm\|$. Let $\Delta_j$ be the Hodge Laplace operator on $j$-forms. For any $p \in (1, \infty)$ and…

We apply techniques from harmonic analysis to study the $L^p$ norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the local bound for the sup norm in terms of the level, which is…

In this article we focus on $L^{p}$ estimates for two types of multilinear lacunary maximal averages over hypersurfaces with curvature conditions. Moreover, we give a different proof for the bilinear lacunary spherical maximal functions. To…

We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In…

In this note we prove that if a sublinear operator T satisfies a certain weighted estimate in the $L^{p}(w)$ space for all $w\in A_{p}$, $1<p<+\infty$, then the operator norm of T on $L^{p}(w)$ is a continuous function of the weight $w$,…

Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincar\'{e} space is found. Also, by means of some estimates for hyperbolic…

Suppose that ${\cal L}$ is a divergence form differential operator of the form ${\cal L}f:=(1/2) e^{U}\nabla_x\cdot\big[e^{-U}(I+H)\nabla_x f\big]$, where $U$ is scalar valued, $I$ identity matrix and $H$ an anti-symmetric matrix valued…

We explore the assignment of norms to $\mathit{\Lambda}$-modules over a finite-dimensional algebra $\mathit{\Lambda}$, resulting in the establishment of normed $\mathit{\Lambda}$-modules. Our primary contribution lies in constructing two…

Let $\mathcal{M}$ be a $\sigma$-finite von Neumann algebra, equipped with a normal faithful state $\varphi$, and let $\mathcal{A}$ be maximal subdiagonal subalgebra of $\mathcal{M}$ and $1\le p<\8$. We prove a Beurling-Blecher-Labuschagne…

We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This…

In this article, we will consider second order uniformly elliptic operators of divergence form defined on R^n with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially…

Let $z = (x,y) \in {\mathbb R}^d \times {\mathbb R}^{N-d}$, with $1 \le d < N$. We prove a priori estimates of the following type :$$\|\Delta\_{x}^{\frac \alpha 2} v \|\_{L^p({\mathbb R}^N)} \lec\_p\Big \| L\_{x } v +…

We establish a new theory of regularity for elliptic complex valued second order equations of the form $\mathcal L=$div$A(\nabla\cdot)$, when the coefficients of the matrix $A$ satisfy a natural algebraic condition, a strengthened version…

For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…

Karapetrovi\'c conjectured that the norm of the Hilbert matrix operator on the Bergman space $A^p_\alpha$ is equal to $\pi/\sin((2+\alpha)\pi/p)$ when $-1<\alpha<p-2$. In this paper, we provide a proof of this conjecture for $0\leq \alpha…

In this paper we connect Calder\'on and Zygmund's notion of $L^p$\- -differentiability with some recent characterizations of Sobolev spaces via the asymptotics of non-local functionals due to Bourgain, Brezis, and Mironescu. We show how the…

We investigate H\"ormander spectral multiplier theorems as they hold on $X = L^p(\Omega),\: 1 < p < \infty,$ for many self-adjoint elliptic differential operators $A$ including the standard Laplacian on $\R^d.$ A strengthened matricial…

We prove sharp uniform $L^p$-bounds for low-lying eigenfunctions of non-self-adjoint semiclassical pseudodifferential operators $P$ on $\mathbb{R}^{n}$ whose principal symbols are doubly-characteristic at the origin of $\mathbb{R}^{2n}$.…