Related papers: L^p estimates for Baouendi-Gru

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…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

We establish $L^p\times L^q$ to $L^r$ estimates for some paraproducts, which arise in the study of the bilinear Hilbert transform along curves.

This is the third part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. For $L$ in some class of elliptic operators, we study weighted norm $L^p$ inequalities for singular…

We will explain how to compute the exact $L^p$ operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a new approach of constructing a sequence of laminates…

In this paper, we study the estimates of resolvents $ R(\lambda,\mathcal{L}_{\varepsilon})=(\mathcal{L}_{\varepsilon}-\lambda I)^{-1} $, where $$ \mathcal{L}_{\varepsilon}=-\operatorname{div}(A(x/\varepsilon)\nabla) $$ is a family of second…

We prove an extrapolation result for general operators under some weak assumptions on the boundedness of the operator. In particular, we show that if the operator is weakly bounded on some L^{p_{0}}(w), for all "flat" weights, w in…

For functions from the set of generalized Poisson integrals $C^{\alpha,r}_{\beta}L_{p}$, $1\leq p <\infty$, we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the…

We obtain weighted mixed inequalities for the first order commutator of singular integral operators in the Schr\"odinger setting. Concretely, for $0<\delta\leq 1$ we give estimates of commutators of Schr\"odinger-Calder\'on-Zygmund…

We establish weighted $L^p$-Fourier-extension estimates for $O(N-k) \times O(k)$-invariant functions defined on the unit sphere $\mathbb{S}^{N-1}$, allowing for exponents $p$ below the Stein-Tomas critical exponent $\frac{2(N+1)}{N-1}$.…

We establish a global weighted $L^p$ estimate for the gradient of the solution to a divergence-form elliptic equations, where the coefficients are in a weighted VMO space and the equations have singularities on a co-dimension two boundary.

In \cite{MR447956}, Muckenhoupt and Wheeden formulated a weighted weak $(p,p)$ inequality where the weight for the weak $L^p$ space is treated as a multiplier rather than a measure. They proved such inequalities for the Hardy-Littlewood…

In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…

We prove weighted strong $q$-variation inequalities with $2<q<\infty$ for differential and singular integral operators. For the first family of operators the weights used can be either Sawyer's one-sided $A^+_p$ weights or Muckenhoupt's…

Although the Bergman projection operator $\mathbf{B}_{\Omega}$ is defined on $L^2(\Omega)$, its behavior on other $L^p(\Omega)$ spaces for $p\not =2$ is an active research area. We survey some of the recent results on $L^p$ estimates on the…

We prove the Hardy-Littlewood-Sobolev type $L^p$ estimates for the gain term of the Boltzmann collision operator including Maxwellian molecule, hard potential and hard sphere models. Combining with the results of Alonso et al. [2] for the…

In this work we show how to get advantage from the Riemann--Hilbert analysis in order to obtain first and second order differential equations for the orthogonal polynomials and associated functions with a weight on the unit circle. We…

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…

We prove $L^p$ estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimates for the general bi-parameter form of the twisted…

We prove new weighted decoupling estimates. As an application, we give an improved sufficient condition for almost everywhere convergence of the Bochner-Riesz means of arbitrary $L^p$ functions for $1<p<2$ in dimensions 2 and 3.