Related papers: Sharp $L^p$-$L^q$ estimates for the spherical harm…

We apply modern techniques of dyadic harmonic analysis to obtain sharp estimates for the Bergman projection in weighted Bergman spaces. Our main theorem focuses on the Bergman projection on the Hartogs triangle. The estimates of the…

A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to $L^p$. This representation is…

We provide $L^p \to L^q$ refinements on some Fourier restriction estimates obtained using polynomial partitioning. Let $S\subset \mathbb{R}^3$ be a compact $C^\infty$ surface with strictly positive second fundamental form. We derive sharp…

We prove new $L^p$-$L^q$-estimates for solutions to elliptic differential operators with constant coefficients in $\mathbb{R}^3$. We use the estimates for the decay of the Fourier transform of particular surfaces in $\mathbb{R}^3$ with…

We prove a sharp integral gradient estimate for harmonic functions on noncompact K\"ahler manifolds. As application, we obtain a sharp estimate for the bottom of spectrum of the p-Laplacian and prove a splitting theorem for manifolds…

Motivared by Carleman's proof of the isoperimetric inequality in the plane, we study some sharp integral inequalities for harmonic functions on the upper halfspace. We also derive the regularity for nonnegative solutions of the associated…

We extend the $L^p$-theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis, allied to new ideas that exploit the radial symmetry of this operator. We are then able…

In this paper, we study the spherical maximal operator $ M_E $ over $ E\subset [1,2]$, restricted to radial functions. In higher dimensions $ d\geq 3$, we establish a complete range of $ L^p-$improving estimates for $ M_E $. In two…

We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…

We prove the $L^p$ regularity of the weighted Bergman projection on the Hartogs triangle, where the weights are powers of the distance to the singularity at the boundary. The restricted range of $p$ is proved to be sharp. By using a…

We establish the $L^p(\mathbb{R}^3)$ boundedness of the helical maximal function for the sharp range $p>3$. Our results improve the previous known bounds for $p>4$. The key ingredient is a new microlocal smoothing estimate for averages…

We prove $L^p-L^q$ Carleman estimates with convex power weights $|x|^\beta$, extending previous work by J. O. Str\"omberg.

A sharp $L^p$ spectral multiplier theorem of Mihlin--H\"ormander type is proved for a distinguished sub-Laplacian on quaternionic spheres. This is the first such result on compact sub-Riemannian manifolds where the horizontal space has…

We demonstrate the $(H^1,L^{1,2})$ or $(L^p,L^{p,2})$ mapping properties of several rough operators. In all cases these estimates are sharp in the sense that the Lorentz exponent 2 cannot be replaced by any lower number.

We prove $L^p\to L^q$ estimates for the local maximal operator associated with dilates of the K\'oranyi sphere in Heisenberg groups. These estimates are sharp up to endpoints and imply new bounds on sparse domination for the corresponding…

In this paper, we establish an improved variable coefficient version of square function inequality, by which the local smoothing estimate $L^p_\alpha\rightarrow L^p$ for the Fourier integral operators satisfying cinematic curvature…

We prove sharp local smoothing estimates for curve averages in all dimensions. As a corollary, we prove the sharp $L^p$ boundedness of the helical maximal operator in $\mathbb{R}^4$, which was previously known only for $\mathbb{R}^2$ and…

We characterize the $L^p-L^q$ boundedness of Bergman-type operators over the Siegel upper half-space. This extends a recent result of Cheng et. al. (Trans. Amer. Math. Soc. 369:8643--8662, 2017) to higher dimensions.

Let $f\in L^p(\mathbb{R}^d)$, $d\ge 3$, and let $A_t f(x)$ the average of $f$ over the sphere with radius $t$ centered at $x$. For a subset $E$ of $[1,2]$ we prove close to sharp $L^p\to L^q$ estimates for the maximal function $\sup_{t\in…

We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the…