Related papers: Two weight inequalities for bilinear forms

By bivariate irreducible representations of ${\rm Sp}(2r)$, we mean irreducible representations with highest weights containing at most two nonzero entries, using the usual identification of dominant weights for complex symplectic Lie…

We answer Totik's question on weighted Bernstein's inequalities showing that $$ \|T_n'\|_{L_p(\omega)} \le C(p,\omega)\, {n}\,\|T_n\|_{L_p(\omega)},\qquad 0<p\le \infty, $$ holds for all trigonometric polynomials $T_n$ and certain…

Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…

We consider L^p two weight inequalities for maximal truncations of dyadic Calderon-Zygmund operators. In the case of one weight being doubling, a characterization is given, and for the general case, sufficient conditions are given,…

We characterize two weight inequalities for general positive dyadic operators. We consider both weak and strong type inequalities, and general (p,q) mapping properties. Special cases include Sawyers Fractional Integral operator results from…

Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\Omega, \mathcal{F}, \mu)$. Then, the following equivalence of norms holds whenever $1 \le q \le p < \infty$…

We prove that bilinear forms associated to the rough homogeneous singular integrals $T_\Omega$ on $\mathbb R^d$, where the angular part $\Omega \in L^q (S^{d-1})$ has vanishing average and $1<q\leq \infty$, and to Bochner-Riesz means at the…

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving $L^p$-averages. This class includes the adjoint forms to the bilinear Hilbert…

We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With $A_1$ weights we improve earlier results of Bourgain, Brezis, and Mironescu.

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geq 0$ and let $V$ be an irreducible rational $G$-module with highest weight $\lambda$. When $V$ is self-dual, a basic question to ask…

We study the vector-valued positive dyadic operator \[T_\lambda(f\sigma):=\sum_{Q\in\mathcal{D}} \lambda_Q \int_Q f \mathrm{d}\sigma 1_Q,\] where the coefficients $\{\lambda_Q:C\to D\}_{Q\in\mathcal{D}}$ are positive operators from a Banach…

In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_\gamma$ on these new function spaces. Furthermore, the…

Let $L$ be a closed, densely defined operator on $L^2(\mathbb{R}^n)$ satisfying suitable $L^p-L^q$ off-diagonal estimates of order $\kappa > 0$. This paper aims to investigate the two-weight estimate and the Bloom weighted estimate for the…

Given a probability space $(\Omega, \mathsf{A}, \mu)$, let $\mathsf{A}_1, \mathsf{A}_2, ...$ be a filtration of $\sigma$-subalgebras of $\mathsf{A}$ and let $\mathsf{E}_1, \mathsf{E}_2, ...$ denote the corresponding family of conditional…

Let $q, r, s \geqslant 1$ satisfy $\frac{1}{2q} + \frac{1}{2r} = \frac{1}{s}$ and $X \in \mathcal{C}_s(\mathcal{H})$. If $(\lambda_n)_{n=1}^{\infty}, (w_n)_{n=1}^{\infty}$ are sequences in $(0,+\infty)$ and $(\lambda_n^{(1-q)/(2q)}…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We obtain new properties of the $q$-analogue of weight multiplicities in finite-dimensional representations of $\mathfrak g$. In particular, it is proved that certain weighted sum of…

We complete our boundedness theory of commutators of bilinear bi-parameter singular integrals by establishing the following result. If $T$ is a bilinear bi-parameter singular integral satisfying suitable $T1$ type assumptions,…

Let $e^{-tL}$ be a analytic semigroup generated by $-L$, where $L$ is a non-negative self-adjoint operator on $L^2(\mathbb{R}^d)$. Assume that the kernels of $e^{-tL}$, denoted by $p_t(x,y)$, only satisfy the upper bound: for all $N>0$,…

We give a short proof of the sharp weighted bound for sparse operators that holds for all $p$, $1<p<\infty$. By recent developments this implies the bounds hold for any Calder\'on-Zygmund operator. The novelty of our approach is that we…

In this paper, we first introduce some new Morrey type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional…