相关论文: Boundedness of a composition of dyadic paraproduct…
We obtain necessary and sufficient conditions to characterize the boundedness of the composition of dyadic paraproduct operators.
When is the composition of paraproducts bounded? This is an important, and difficult question, related to to a question of Sarason on composition of Hankel matrices, and the two-weight problem for the Hilbert transform. We consider…
In this paper, we show that dyadic paraproducts $\pi_b$ with $b$ in dyadic BMO are bounded on matrix weighted $L^p(W)$ if $W$ is a matrix $\text{A}_p$ weight.
We prove L^p estimates for a two-dimensional bilinear operator of paraproduct type. This result answers a question posed by Demeter and Thiele in [3].
In this note, we investigate the sharpness of existing bounds for various types of bi-parameter paraproducts acting between product Hardy spaces in the dyadic setting. We show that these bounds are sharp in most cases but fail to be so in…
We show the existence of $(\epsilon,n)$-complements for $(\epsilon,\mathbb{R})$-complementary surface pairs when the coefficients of boundaries belong to a DCC set.
In this paper we offer alternate upper bound for the operator $\Pi_b^*\Pi_d$ to the ones present in literature, thus extending the known upper bounds from the $L^2(\mathbb{R})$ setting to $L^p(w)$, for $1<p<\infty,$ and a Muckenhoupt weight…
In this article, we investigate the boundedness properties of the multilinear dyadic paraproduct operators in the weighted setting. We also obtain weighted estimates for the multilinear Haar multipliers and their commutators with dyadic BMO…
The dyadic paraproduct is bounded in weighted Lebesgue spaces $L_p(w)$ if and only if the weight $w$ belongs to the Muckenhoupt class $A_p^d$. However, the sharp bounds on the norm of the dyadic paraproduct are not known even in the…
In this note, we prove that separable subgroups have bounded packing in ambient groups. The notion bounded packing was introduced by Hruska and Wise and in particular, our result answers positively a question of theirs, asking whether each…
We prove bounds in the local $ L^2 $ range for exotic paraproducts motivated by bilinear multipliers associated with convex sets. One result assumes an exponential boundary curve. Another one assumes a higher order lacunarity condition.
We investigate boundedness of hyperbolic components in the moduli space of Newton maps. For quartic maps, (i) we prove hyperbolic components possessing two distinct attracting cycles each of period at least two are bounded, and (ii) we…
Theory of $n$-complements with applications is presented.
We introduce multilinear analogues of dyadic paraproduct operators and Haar Multipliers, and study boundedness properties of these operators and their commutators. We also characterize dyadic BMO functions via the boundedness of certain…
We prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.
We establish the boundedness character of solutions of a system of rational difference equations with a variable coefficient
We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in…
We study a family of variants of Erd\H os' unit distance problem, concerning distances and dot products between pairs of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, we look for…
In this paper, we study the Seiberg-Witten equations on the product R x Y, where Y is a compact 3-manifold with boundary. Following the approach of Salamon and Wehrheim in the instanton case, we impose Lagrangian boundary conditions for the…
We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…