Related papers: Dyadic triangular Hilbert transform of two general…
The finite Hilbert transform $T$ is a classical (singular) kernel operator which is continuous in every rearrangement invariant space $X$ over $(-1,1)$ having non-trivial Boyd indices. For $X=L^p$, $1<p<\infty$, this operator has been…
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
We prove the $L^p$ boundedness of a maximal operator associated with a dyadic frequency decomposition of a Fourier multiplier, under a weak regularity assumption.
In singularity theory or algebraic geometry, it is natural to investigate possible Hilbert functions for special algebras $A$ such as local complete intersections or more generally Gorenstein algebras. The sequences that occur as {the}…
The optimal $L^p \to L^q$ mapping properties for the (local) helical maximal function are obtained, except for endpoints. The proof relies on tools from multilinear harmonic analysis and, in particular, a localised version of the…
We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
Maximal angular operator sends a function defined in a sector of the complex plane to a Maximal angular operator sends a function defined in a sector of the complex plane with vertex at 0 to the function of modulus obtained by maximizing…
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…
Jacobi elliptic functions and complete elliptic integrals are generalized using three parameters. These generalized functions and integrals are closely related to ordinary differential equations involving $p$-Laplacian. In this paper,…
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…
In this paper we prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted $L^p$…
The classical $L^2$ estimate for the $\overline{\partial}$ operators is a basic tool in complex analysis of several variables. Naturally, it is expected to extend this estimate to infinite dimensional complex analysis, but this is a…
We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our…
We establish a new natural extension of Mittag-Leffler function with three variables which is so called "trivariate Mittag-Leffler function". The trivariate Mittag-Leffler function can be expressed via complex integral representation by…
This paper considers the problem of $L^p$-estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of such objects are ubiquitous in the study of Fourier restriction…
We construct the Dirichlet form associated with the dynamical $\Phi^4_3$ model obtained in [Hai14, CC13] and [MW16]. This Dirichlet form on cylinder functions is identified as a classical gradient bilinear form. As a consequence, this…
We prove certain endpoint restriction estimates for the paraboloid over finite fields in three and higher dimensions. Working in the bilinear setting, we are able to pass from estimates for characteristic functions to estimates for general…
In this article, we address endpoint issues for the bilinear spherical maximal functions. We obtain borderline restricted weak type estimates for the well studied bilinear spherical maximal function…
We introduce sufficient conditions on discrete singular integral operators for their maximal truncations to satisfy a sparse bound. The latter imply a range of quantitative weighted inequalities, which are new. As an application, we prove…