Related papers: On Muckenhoupt-Wheeden Conjecture

A conjecture of May states that there is an up-to-adjunction strictification of symmetric bimonoidal functors between bipermutative categories. The main result of this paper proves a weaker form of May's conjecture that starts with…

The purpose of this note is to show that the di-bar-estimate which is needed in the Ohsawa-Takegoshi Extension Theorem [6] is a direct consequence of the Hormander-Kohn-Morrey weigthed inequality. In this inequality, the Donnelly-Fefferman…

In the previous author's paper the Macdonald norm conjecture (including the famous constant term conjecture) was proved. This paper contains the proof of the remaining two (the duality and evaluation conjectures). The evaluation theorem is…

We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that $$\Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, \|f\|_{L^1(uv)},$$…

We show that $\kgl$-linear cohomology theories over an affine Dedekind scheme $S$ admit a canonical weight filtration on resolvable motives without inverting residual characteristics. Combined with upcoming work of Annala--Hoyois--Iwasa,…

In this paper, our aim is to show some mean value inequalities for the Fox-Wright functions, such as Tur\'an--type inequalities, Lazarevi\'c and Wilker--type inequalities. As applications we derive some new type inequalities for…

We characterize two-weight norm inequalities for potential type integral operators in terms of Sawyer-type testing conditions. Our result is stated in a space of homogeneous type with no additional geometric assumptions, such as group…

In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolff's potential. A refinement of the Carleson embedding theorem is also introduced.…

Let $\mathsf M$ and $\mathsf M _{\mathsf S}$ respectively denote the Hardy-Littlewood maximal operator with respect to cubes and the strong maximal operator on $\mathbb{R}^n$, and let $w$ be a nonnegative locally integrable function on…

For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^1(\widetilde{M}w)$ into weak--$L^1(w)$. Our main innovation is that $\widetilde{M}$ is a maximal function…

We derive formulas for the Fourier coefficients of $|f|^2$, where $f(z_1,z_2)=(1-\frac{z_1+z_2}{r})^{-\alpha}$, in terms of hypergeometric functions. Using these formulas we provide additional counterexamples to the weak Shanks conjecture,…

We characterize the weak-type boundedness of the Hilbert transform $H$ on weighted Lorentz spaces $\Lambda^p_u(w)$, with $p>0$, in terms of some geometric conditions on the weights $u$ and $w$ and the weak-type boundedness of the…

Given a nonnegative function $\psi : \N \to \R $, let $W(\psi)$ denote the set of real numbers $x$ such that $|nx -a| < \psi(n) $ for infinitely many reduced rationals $a/n (n>0) $. A consequence of our main result is that $W(\psi)$ is of…

In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…

The purpose of this paper is to develop a new theory of gauges in mixed characteristic. Namely, let $k$ be a perfect field of characteristic $p>0$ and $W(k)$ the $p$-typical Witt vectors. Making use of Berthelot's arithmetic differential…

We provide a Fefferman-Stein type weighted inequality for maximally modulated Calder\'on-Zygmund operators that satisfy \textit{a priori} weak type unweighted estimates. This inequality corresponds to a maximally modulated version of a…

In this paper we prove a reverse H\"{o}lder inequality for the variable exponent Muckenhoupt weights $\mathcal{A}_{p(\cdot)}$, introduced by the first author, Fiorenza, and Neugeabauer. All of our estimates are quantitative, showing the…

In this paper, we establish a class of Stein-Weiss type inequality with partial variable weight functions on the upper half space using a weighted Hardy type inequality. Overcoming the impact of weighted functions, the existence of extremal…

The matroidal version of the Merino--Welsh conjecture states that the Tutte polynomial $T_M(x,y)$ of any matroid $M$ without loops and coloops satisfies that $$\max(T_M(2,0),T_M(0,2))\geq T_M(1,1).$$ Equivalently, if the Merino--Welsh…

The purpose of this note is to extend the extrapolation result by by Cruz-Uribe Martell and P\'erez as follows. Given a family $\mathcal{F}$ of pairs of functions suppose that for some $0<p<\infty$ and for every $w\in A_{\infty}$…