Related papers: Bilinear pseudo-differential operators with exotic…
The boundedness from $H^p \times L^2$ to $L^r$, $1/p+1/2=1/r$, and from $H^p \times L^{\infty}$ to $L^p$ of bilinear pseudo-differential operators is proved under the assumption that their symbols are in the bilinear H\"ormander class…
We consider the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander classes $BS_{\rho, \rho}^m$, $0 < \rho < 1$. In this paper, we show that the condition $1/p = 1/p_1 + 1/p_2$ is necessary when we consider the…
We consider bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class, $BS_{\rho, \rho}^m$, $m \in \mathbb{R}$, $0 \leq \rho < 1$. The aim of this paper is to discuss low regularity conditions for symbols to…
We extend the known result that the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{-n/2}_{0,0}(\mathbb{R}^n)$ are bounded from $L^2 \times L^2$ to $h^1$. We show that those operators are also…
This paper investigates the boundedness of bilinear pseudo-differential operators with symbols in the H\"{o}rmander class $BS_{\varrho,\delta}^m(\mathbb{R}^n)$ in the previously unexplored regime $0 \leq \varrho < \delta < 1$. We establish…
In the present paper, bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^m_{0,0}$ are considered. In particular, the boundedness of these operators on Sobolev spaces is established. Our main result is…
In this short note, we consider bilinear pseudo-differential operators with symbols belonging to the Sj\"ostrand class. We show that those operators are bounded from the product of the $L^2$-based Sobolev spaces $H^{s_1} \times H^{s_2}$ to…
Boundedness properties for pseudodifferential operators with symbols in the bilinear H\"ormander classes of sufficiently negative order are proved. The results are obtained in the scale of Lebesgue spaces and, in some cases, end-point…
In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class $BS_{1,1}^m$, when both arguments belong to Triebel-Lizorkin spaces of the type $F_{p,q}^{n/p}(\mathbb{R}^n)$. The inequalities are…
We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…
We extend and improve the known results about the boundedness of the bilinear pseudo-differential operators with symbols in the bilinear H\"ormander class $BS^{m}_{0,0}(\mathbb{R}^n)$. We consider wider classes of symbols and improve…
In this paper, we study the boundedness of pseudodifferential operators with symbols in the H\"ormander class $S^0_{\rho,\rho}$ on $\alpha$-modulation spaces $M_{p,q}^{s,\alpha}$, and consider the relation between $\alpha$ and $\rho$. In…
The multilinear pseudo-differential operators with symbols in the multilinear H\"ormander class $S_{0,0}$ are considered. A complete identification of the cases where those operators define bounded operators between local Hardy spaces is…
In this paper, we explore a specific class of bi-parameter pseudo-differential operators characterized by symbols $\sigma(x_1,x_2,\xi_1,\xi_2)$ falling within the product-type H\"ormander {class} $\mathbf{S}^m_{\rho, \delta}$. This…
Bilinear pseudodifferential operators with symbols in the bilinear analog of all the H\"ormander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise…
We consider the multilinear pseudo-differential operators with symbols in a generalized $S_{0,0}$-type class and prove the boundedness of the operators from $(L^2,\ell^{q_1}) \times \dots \times (L^2,\ell^{q_N})$ to $(L^2,\ell^{r})$, where…
We extended the known result that symbols from modulation spaces $M^{\infty,1}(\mathbb{R}^{2n})$, also known as the Sj\"{o}strand's class, produce bounded operators in $L^2(\mathbb{R}^n)$, to general $L^p$ boundedness at the cost of lost of…
In this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{\rho,\delta}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{\rho,\delta}^m) \subset…
In this paper, the ranges of bilinear pseudo-differential operators of $S_{0,0}$-type on $L^2 \times L^2$ are determined in the framework of Besov spaces. Our result improves the $L^2 \times L^2 \to L^1$ boundedness of those operators with…
In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for H\"ormander classes of pseudo-differential…