Related papers: Square function estimates and Local smoothing for …

Weighted quadratic estimates are proved for certain bisectorial firstorder differential operators with bounded measurable coefficients which are (not necessarily pointwise) accretive, on complete manifolds with positive injectivity radius.…

A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of $L^{p}-$multipliers, a rather general inequality…

In this paper, we will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\lambda$-function on the weighted Herz spaces $\dot…

Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current…

Let $0<\sigma<n/2$ and $H=(-\Delta)^\sigma +V(x)$ be Schr\"odinger type operators on $\mathbb R^n$ with a class of scaling-critical potentials $V(x)$, which include the Hardy potential $a|x|^{-2\sigma}$ with a sharp coupling constant $a\ge…

A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…

For a split reductive group $G$ over a number field $k$, let $\rho$ be an $n$-dimensional complex representation of its complex dual group $G^\vee(\mathbb{C})$. For any irreducible cuspidal automorphic representation $\sigma$ of…

Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi stable real (or complex) Frechet algebras.

We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy--Littlewood--Sobolev theorem in this context. In our main result, we investigate the dependence of…

The Fourier transforms of the products of two respectively three solutions of the free Schroedinger equation in one space dimension are estimated in mixed and, in the first case weighted, L^p - norms. Inserted into an appropriate variant of…

This paper is dedicated to studying pointwise estimates of the fundamental solution for the higher order Schr\"{o}dinger equation: % we investigate the fundamental solution of the higher order Schr\"{o}dinger equation…

In the context of global optimization and mixed-integer non-linear programming, generalizing a technique of D'Ambrosio, Fampa, Lee and Vigerske for handling the square-root function, we develop a virtuous smoothing method, using cubics,…

We improve a result of Lau and Zhao on the variance of Fourier coefficients of primitive cuspidal modular forms for SL2(Z) in arithmetic progressions. This is achieved by using bounds on the first moment of Rankin-Selberg L-functions in the…

We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in $\mathbb{R}^n$ for $n \geq 3$. This demonstrates a limitation…

We show that on compact Riemann surfaces of nonpositive curvature, the generalized periods, i.e. the $\nu$-th order Fourier coefficients of eigenfunctions $e_\lambda$ over a closed smooth curve $\gamma$ which satisfies a natural curvature…

In this paper, we prove the local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. As applications, we obtain Liouville type…

For functions $f$ with Fourier transform supported in the truncated cone, we bound superlevel sets $\{x\in\mathbb{R}^3:|f(x)|>\alpha\}$ using an $\alpha$-dependent version of the wave envelope estimate of Guth--Wang--Zhang. Our estimates…

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge--Dirac operator on…

For a class of sparse operators including majorants of singular integral, square function, and fractional integral operators in a uniform manner, we prove off-diagonal two-weight estimates of mixed type in the two-weight and…