Related papers: Note about square function estimates and uniformly…

We consider Mertens' function M(x,q,a) in arithmetic progression, Assuming the generalized Riemann hypothesis (GRH), we show an upper bound that is uniform for all moduli which are not too large. For the proof, a former method of K.…

We prove a general result implying the $L^2$ stability of Haar decompositions of $L^2({\bf R}^d)$ functions when the Haar functions are distorted by arbitrary, independent, affine changes of variable that are close to the identity. We apply…

We use the Bellman function method to give an elementary proof of a sharp weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the weight and in the complexity of the shift. Together with the representation of a…

We consider a generalized form of certain integral inequalities given by Guessab, Schmeisser and Alomari. The trapezoidal, mid point, Simpson, Newton-Simpson rules are obtained as special cases. Also, inequalities for the generalized…

We give a new proof of Milne's formulas for the number of representations of an integer as a sum of 4m^2 and 4m(m+1) squares. The proof is based on explicit evaluation of pfaffians with elliptic function entries, and relates Milne's…

We study, in $L^{1}(\R^n;\gamma)$ with respect to the gaussian measure, non-tangential maximal functions and conical square functions associated with the Ornstein-Uhlenbeck operator by developing a set of techniques which allow us, to some…

We offer some new applications of an extension of Abel's lemma, as well as its more general form established by Andrews and Freitas. A nice connection is established between this lemma and series involving the Riemann zeta function.

We consider self-adjoint semigroups $T_t = \exp(-tA)$ acting on $L^2(\Omega)$ and satisfying (generalised) Gaussian estimates, where $\Omega$ is a metric measure space of homogeneous type of dimension $d$. The aim of the article is to show…

In this paper we show that if $\mu$ is any locally and uniformly $\alpha$-dimensional measure supported on a $\alpha$-quasi-regular set $E$, then $L^2(\mu)$ admits a frame of exponentials. In particular, for the uniform middle third Cantor…

We prove three sharp estimates for the generalized Zalcman coefficient functional: one for the Hurwitz class, another for the Noshiro-Warschawski class, and yet another for the functions in the closed convex hull of convex univalent…

Let $P(\Delta)$ be a polynomial of the Laplace operator $\Delta=\sum_{j=1}^n\frac{\partial^2}{\partial x^2_j}$ on $\mathbb{R}^n$. We prove the existence of weak solutions of the equation $P(\Delta)u=f$ and the existence of a bounded right…

A new set of symmetric correction functions is presented for high-order flux reconstruction, that expands upon, while incorporating, all previous correction function sets and opens the possibility for improved performance. By considering FR…

For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper…

We improve local smoothing estimates for fractional Schr\"{o}dinger equations for $\alpha \in (0,1) \cup (1,\infty)$.

Let $M(\alpha)$ denote the Mahler measure of the algebraic number $\alpha$. In a recent paper, Dubickas and Smyth constructed a metric version of the Mahler measure on the multiplicative group of algebraic numbers. Later, Fili and the…

We show that the Lusin area integral or the square function on the unit ball of $\C^n$, regarded as an operator in weighted space $L^2(w)$ has a linear bound in terms of the invariant $A_2$ characteristic of the weight. We show a…

Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…

In this short note we establish an integral geometric inequality in a smooth metric measure space of the nonnegative Bakry-\'Emery Ricci curvature. This result can be regarded as a mild generalization of the almost Schur theorem due to De…

Using techniques from integrable systems, we obtain a number of exact results for random partitions. In particular, we prove a simple formula for correlation functions of what we call the Schur measure on partitions (which is a far reaching…

The ring of symmetric functions $\Lambda$, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the…