Related papers: Boundedness of some multi-parameter fiber-wise mul…

Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$…

We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm…

We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…

We give various conditions for Hermite pseudo-multipliers to be bounded on $L^2(\mathbb{R}^n)$. As a by-product we also give results on $L^p(\mathbb{R}^n)$, as well as new results for pseudo-multipliers for the Gaussian measure setting. One…

M. Lacey and C. Thiele proved in [27] (Annals of Math. (1997)) and [28] (Annals of Math. (1999)) that the bilinear Hilbert transform maps $L^{p_1}\times L^{p_2}\rightarrow L^{p}$ boundedly when $\frac{1}{p_1}+\frac{1}{p_2}=\frac{1}{p}$ with…

We study a parametrized family of strong maximal fractional operators. We prove their $L^p$ to $L^q$ boundedness for $1<p\le q<\infty$.

In this paper we investigate the mapping properties of periodic Fourier integral operators in $L^p(\mathbb{T}^n)$-spaces. The operators considered are associated to periodic symbols (with limited regularity) in the sense of Ruzhansky and…

In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from $L^{\vec{p}}\left(T_B\times T_B, dV_{\alpha_1}\times dV_{\alpha_2}\right)$ to $L^{\vec{q}}\left(T_B\times T_B, dV_{\beta_1}\times…

We establish Littlewood-Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem for operator-valued multipliers. We also show two-weight…

We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…

In this paper, we characterize the multiple operator integrals mappings which are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is…

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…

In this note we study the $L^p-L^q$ boundedness of Fourier multipliers of anharmonic oscillators, and as a consequence also of spectral multipliers, for the range $1<p \leq 2 \leq q <\infty$. The underlying Fourier analysis is associated…

We consider BMO spaces of operator-valued functions, among them the space of operator-valued functions $B$ which define a bounded paraproduct on $L^2(H)$. We obtain several equivalent formulations of $\|\pi_B\|$ in terms of the norm of the…

We give a class of Fourier multipliers with non-symmetric symbols and explicit norm bounds on $L^p$ spaces by using the stochastic calculus of L\'evy processes and Burkholder-Wang estimates for differentially subordinate martingales.

We consider the weighted $A^p(\omega)$ and $B_p(\omega)$ spaces of holomorphic functions on the polydisk (in the case of $p>1$). We prove some theorems about the boundedness of Toeplitz operators on weighted Besov spaces $B_p(\omega)$ and…

We obtain $L^p$ estimates for Toeplitz operators on the generalized Hartogs triangles $\mathbb{H}_\gamma = \{(z_1,z_2) \in \mathbb{C}^2: |z_1|^\gamma < |z_2|<1\}$ for two classes of positive radial symbols, one a power of the distance to…

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…

In this paper, we investigate the H\"ormander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by $L^u$-based Sobolev norms for $1<u\le 2$ , our results on the smoothness…

We prove $L^p\times L^q\rightarrow L^r$ bounds for certain lacunary bilinear maximal averaging operators with parameters satisfying the H\"older relation $1/p+1/q=1/r$. The boundedness region that we get contains at least the interior of…