Related papers: $L^p$ estimates for the biest I. The Walsh case

The paper makes the first steps into the study of extensions ("twisted sums") of noncommutative $L^p$-spaces regarded as Banach modules over the underlying von Neumann algebra $\mathcal M$. Our approach combines Kalton's description of…

Let $P$ denote the $3$-dimensional paraboloid over a finite field of odd characteristic in which $-1$ is not a square. We show that the Fourier extension operator associated with $P$ maps $L^2$ to $L^{r}$ for $r > \frac{32}{9} \approx…

In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to…

We prove some Sawyer-type characterizations for multilinear fractional maximal function for the upper triangle case. We also provide some two-weight norm estimates for this operator. As one of the main tools, we use an extension of the…

Operators such as Carleson operator are known to be bounded on $L^p$ for all $1<p<\infty$, but not from $L^1$ to weak-$L^1$ and from $H^p$ to $L^p$ for each $0<p\leq 1$, the object of this article is to give a estimate for all $0<p<\infty$.…

The authors use steepest descent ideas to obtain a priori $L^p$ estimates for solutions of Riemann-Hilbert Problems. Such estimates play a crucial role, in particular, in analyzing the long-time behavior of solutions of the perturbed…

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.

We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le…

We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…

In this paper, optimal $L^p-L^q$ estimates are obtained for operators which average functions over polynomial submanifolds, generalizing the $k$-plane transform. An important advance over previous work is that full $L^p-L^q$ estimates are…

We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…

We find a minimal notion of non-degeneracy for bilinear singular integral operators $T$ and identify testing conditions on the multiplying function $b$ that characterize the $L^p\times L^q\to L^r,$ $1<p,q<\infty$ and $r>\frac{1}{2},$…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

Given a smooth bump function, we consider the multiplier formed by taking the linear combination of the translations of the bump function and the corresponding bilinear Fourier multiplier operator. Under certain condition on the bump…

Let $BV_p[0,1]$, $1\le p<\infty$, be the Banach algebra of functions of bounded $p$-variation in the sense of Wiener. Recently, Kowalczyk and Turowska \cite{KT19} proved that the multiplication in $BV_1[0,1]$ is an open bilinear mapping. We…

This paper is a successor of \cite{laceyt}. In that paper we considered bilinear operators of the form H_alpha(f_1,f_2)(x) = p.v. \int f_1(x-t) f_2(x + alpha t)/t dt, which are originally defined for f_1, f_2 in the Schwartz class S(R). The…

We provide asymptotically sharp bounds for the $L_p$ norms of the Fourier multipliers with the symbols $e^{i\lambda \varphi(\xi/|\xi|)}$, where $\lambda\in \mathbb{R}$ is a large parameter.

For multiparameter bilinear paraproduct operators $B$ we prove the estimate $$ B: L^p X L^q --> L^r, 1<p,q\le{}\infty. $$ Here, $1/p+1/q=1/r$ and special attention is paid to the case of $0<r<1$. (Note that the families of multiparameter…

The aim of this work is the study of the Weinstein $L^2$- multiplier operators on $\mathbb{R}^{d+1}_+$ and we give for them Calder\'on's reproducing formulas and best approximation using the theory of Weinstein transform and reproducing…

We prove the applicability of the finite section method to an arbitrary operator in the Banach algebra generated by the operators of multiplication by piecewise continuous functions and the convolution operators with symbols in the algebra…