Related papers: Entropy conditions in two weight inequalities for …

This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…

We consider weighted operators acting on $L^p(\mathbb{R}^d)$ and show that they depend continuously on the weight $w\in A_p(\mathbb{R}^d)$ in the operator topology. Then, we use this result to estimate $L^p_w(\mathbb{T})$ norm of…

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…

Over the past few years, a family of interesting new inequalities for the entropies of sums and differences of random variables has been developed by Ruzsa, Tao and others, motivated by analogous results in additive combinatorics. The…

In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \mu be a Borel measure on \R^d which may be non doubling. The only condition that \mu must satisfy is \mu(B(x,r))\leq Cr^n for…

Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…

We provide an essentially complete dictionary of all implications among the basic and fundamental conditions in weighted theory such as the doubling, one weight A_p(w), A_\infty and C_p conditions as well as the two weight A_p and the…

We prove strong-type $A_p$-$A_\infty$ estimate for square functions, improving on the $ A_p$ bound due to Lerner. Entropy bounds, in the recent innovation of Treil-Volberg, are then proved. The techniques of proof include parallel stopping…

Matrix weights satisfying a Muckenhoupt $A_p$-condition relative to a family of anisotropic balls in $\mathbb{R}^d$ defined by a pseudo-metric are studied. It is shown that such matrix weights satisfy a doubling condition and a reverse…

We present new results on the two-weighted boundedness of singular integral operators and $L^p$ boundedness of the Orlicz maximal function. Namely, we extend a theorem of P\'erez regarding the necessary and sufficient conditions for the…

The main objective of this work is to bring together two well known and, a priori, unrelated theories dealing with weighted inequalities for the Hardy-Littlewood maximal operator $M$, and thus, we consider the boundedness of $M$ in the…

We propose an alternative refined de Sitter conjecture. It is given by a natural condition on a combination of the first and second derivatives of the scalar potential. We derive our conjecture in the same weak coupling, semi-classical…

A conjecture -- \emph{the modified super-additivity inequality} of relative entropy -- was proposed in \cite{Zhang2012}: There exist three unitary operators $U_A\in \unitary{\cH_A},U_B\in \unitary{\cH_B}$, and $U_{AB}\in \unitary{\cH_A\ot…

Let $A_i$ for $i=1, 2$ be an expansive dilation, respectively, on ${\mathbb R}^n$ and ${\mathbb R}^m$ and $\vec A\equiv(A_1, A_2)$. Denote by ${\mathcal A}_\infty(\rnm; \vec A)$ the class of Muckenhoupt weights associated with $\vec A$. The…

In this paper we consider two weight bump conditions for higher order commutators. Given $b$ and a Calder\'on-Zygmund operator $T$, define the commutator $T^1_bf=[T,b]f= bTf-T(bf)$, and for $m\geq 2$ define the iterated commutator $T^m_b f…

We prove several sharp weighted norm inequalities for commutators of classical operators in harmonic analysis. We find sufficient $A_p$-bump conditions on pairs of weights $(u,v)$ such that $[b,T]$, $b\in BMO$ and $T$ a singular integral…

We define a Muckenhoup-type condition on weighted Morrey spaces using the K\"othe dual of the space. We show that the condition is necessary and sufficient for the boundedness of the maximal operator defined with balls centered at the…

We improve bump conditions for the two-weight boundedness of Calder\'on-Zygmund operators introduced recently by R. Rahm and S. Spencer.

As is known, the class of weights for Morrey type spaces $\mathcal{L}^{p,\lb}(\rn) $ for which the maximal and/or singular operators are bounded, is different from the known Muckenhoupt class $A_p$ of such weights for the Lebesgue spaces…

We prove new sufficient bump conditions for general iterated commutators of Calder\'on-Zygmund operators and fractional integral operators. As an application of our results we derive two weight compactness theorems for higher order iterated…