Related papers: A description of $A_{\infty }$-weights for VMO

We prove weighted mixed-norm $L^q_t(W^{2,p}_x)$ and $L^q_t(C^{2,\alpha}_x)$ estimates for $1<p,q<\infty$ and $0<\alpha<1$, weighted mixed weak-type estimates for $q=1$, $L^\infty_{t}(L^p_x)-BMO_t(W^{2,p}_x)$, and…

In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of…

Let $\mathcal{L}$ be a Schr\"odinger operator of the form $\mathcal{L}=-\Delta+V$ acting on $L^2(\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\"older class ${RH}_q$ for some $q\geq (n+1)/2$. Let…

We characterize the Carleson measures for an exponential Bergman space on the unit ball of $\mathbb C^n$ in terms of the ball induced by the complex Hessian of the logarithm of the weight function. The boundedness (or compactness) of…

Part of the intrinsic structure of singular integrals in the Bessel setting is captured by Muckenhoupt-type weights. Anderson--Kerman showed that the Bessel Riesz transform is bounded on weighted $L^p_w$ if and only if $w$ is in the class…

We give analytic description for the completion of $C_0^\infty ( \mathbf{R}_+)$ in Dirichlet space $D^{1,p}(\mathbf{R}_+, \omega):= \{ u:\mathbf{R}_+\rightarrow \mathbf{R}: u\ \hbox{ is locally absolutely continuous on} \ \mathbf{R}_+ \…

Grafakos systematically proved that $A_\infty$ weights have different characterizations for cubes in Euclidean spaces in his classical text book. Very recently, Duoandikoetxea, Mart\'{\i}n-Reyes, Ombrosi and Kosz discussed several…

We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result…

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion…

Given a finite positive Borel measure $\mu$ in the open unit disc of the complex plane, we construct a bounded outer function $E$ whose boundary values have vanishing mean oscillation such that $|E| \mu$ is a vanishing Carleson measure. As…

Let $\omega$ be a B\'ekoll\'e-Bonami weight. We give a complete characterization of the positive measures $\mu$ such that $$\int_{\mathcal H}|M_\omega f(z)|^qd\mu(z)\le C\left(\int_{\mathcal H}|f(z)|^p\omega(z)dV(z)\right)^{q/p}$$ and…

In this paper we construct a wavelet basis in weighted L^2 of Euclidean space possessing vanishing moments of a fixed order for a general locally finite positive Borel measure. The approach is based on a clever construction of Alpert in the…

In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set $E\subset\mathbb{R}$ satisfies $d(\cdot,E)^{-\alpha}\in A_1^+(\mathbb{R})\cap L^1_\textrm{loc}(\mathbb{R})$ for some…

We give an alternative characterization of the class of Muckenhoupt weights $A_{\infty, \mathfrak B}$ for homothecy invariant Muckenhoupt bases $\mathfrak B$ consisting of convex sets. In particular we show that $w\in A_{\infty, \mathfrak…

The balayage of a Carleson measure lies of course in BMO. We show that the converse statement is false. We also make a two-sided estimate of the Carleson norm of a positive measure in terms of balayages.

Let $L$ be a divergence form elliptic operator with complex bounded measurable coefficients, $\omega$ a positive concave function on $(0,\infty)$ of strictly critical lower type $p_\omega\in (0, 1]$ and…

The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems…

Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \infty$, and $T$ be any of the Riesz transforms. We will characterize the boundedness of the commutator $[T, B]$ on $L^p(W)$ in terms of the…

We provide characterizations of Carleson measures on a certain class of bounded pseudoconvex domains. An example of a vanishing Carleson measure whose Berezin transform does not vanish on the boundary is given in the class of the Hartogs…

This is the first part of a series of three articles. In this paper, we obtain weighted norm inequalities for different conical square functions associated with the Heat and the Poisson semigroups generated by a second order divergence form…