Related papers: The Walsh model for $M_2^{*}$ Carleson
We prove when a Banach ideal of linear operators defined, or characterized, by the transformation of vector-valued sequences is maximal. Known results are recovered as particular cases and new information is obtained. To accomplish this…
In this article we provide new applications for exponential approximation using the framework of Pek\"oz and R\"ollin (in press), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process…
We show how to derive (variants of) Michell truss theory in two and three dimensions rigorously as the vanishing weight limit of optimal design problems in linear elasticity in the sense of $\Gamma$-convergence. We improve our previous…
We prove $L^p$ bounds, $\frac{d^2 + 4d + 2}{(d+1)^2} < p < 2(d+1)$, for maximal linear modulations of singular integrals along paraboloids with frequencies in certain subspaces of $\mathbb{R}^{d+1}$, for $d \geq 2$. This generalizes…
A formulation of the Carleson embedding theorem in the multilinear setting is proved which allows to obtain a multilinear analogue of Sawyer's two weight theorem for the multisublinear maximal function \mathcal{M} introduced in Lerner et…
We give a simplified and direct proof of the Kato square root estimate for parabolic operators with elliptic part in divergence form and coefficients possibly depending on space and time in a merely measurable way. The argument relies on…
We prove $L^p$ bounds in the range $1<p<\infty$ for a maximal dyadic sum operator on $\rn$. This maximal operator provides a discrete multidimensional model of Carleson's operator. Its boundedness is obtained by a simple twist of the proof…
The Bessel operator, that is, the Schr\"odinger operator on the half-line with a potential proportional to $1/x^2$, is analyzed in the momentum representation. Many features of this analysis are parallel to the approach \`a la K. Wilson to…
We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…
Evaluation of the Bellman functions is a difficult task. The exact Bellman functions of the dyadic Carleson Embedding Theorem 1.1 and the dyadic maximal operators are obtained in [3] and [4]. Actually, the same Bellman functions also work…
In this paper, we study the large time behavior of solutions of a class of parabolic fully nonlinear integro-differential equations in a periodic setting. In order to do so, we first solve the ergodic problem}(or cell problem), i.e. we…
In this paper we formulate embedding maps into time-frequency space related to the Carleson operator and its variational counterpart. We prove bounds for these embedding maps by iterating the outer measure theory of [DT15]. Introducing…
We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.
We prove a weak-$L^p$ bound for the Walsh-Carleson operator for $p $ near 1, improving on a theorem of Sjolin. We relate our result to the conjectures that the Walsh-Fourier and Fourier series of a function $f\in L\log L(\mathbb T)$…
In this work, we explore the application of multilinear algebra in reducing the order of multidimentional linear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system…
In this paper, we propose a novel kind of numerical approximations to inherit the ergodicity of stochastic Maxwell equations. The key to proving the ergodicity lies in the uniform regularity estimates of the numerical solutions with respect…
Lacunary trigonometric and Walsh series satisfy limiting results that are typical for i.i.d. random variables such as the central limit theorem (Salem, Zygmund 1947), the law of the iterated logarithm (Weiss 1959) and several probability…
We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights $\varphi_{t,\gamma}(\tau)=|(\tau-t)^\gamma|$, where $\gamma$ is a complex number, over arbitrary Carleson curves. If the…
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…