69 papers
The paper demonstrates that every Hardy field can be extended to an -free Hardy field, a result that connects to classical oscillation criteria and is used to resolve questions posed by Boshernitzan and generalize one of his theorems.
This paper investigates the distribution of zeros for a specific class of polynomials and their derivatives, ultimately proving a weak variant of Sendov's conjecture for polynomials whose zeros are real and share the same sign.
This paper introduces a flexible transformed minimization model with two adjustable parameters to enhance sparse signal recovery, establishing exact and stable recovery guarantees via the restricted isometry property, proposing an efficient IRLSTLp algorithm with convergence proofs, and demonstrating its superior performance and theoretical bounds through numerical experiments.
This paper establishes convex body domination results for generalized vector-valued commutators of operators that already admit such domination, deriving strong type estimates and characterizing the associated BMO spaces.
This paper establishes a new boundedness criterion for the maximal operator on variable Lebesgue spaces, formulated in terms of a variable exponent analogue of the weighted condition.
The paper demonstrates that Brascamp-Lieb constants are semi-algebraic functions of their feasible data, satisfying a polynomial relation, and extends this algebraicity result to the broader context of quiver Brascamp-Lieb constants associated with bipartite quivers.
This paper establishes a universal inequality for discrete cumulative Riemann sums of decreasing functions, demonstrating that the bound arises from a distribution-free continuous identity and unifying its interpretation through Riemann sums, Abel summation, and majorization theory.
This paper generalizes the classical discrete -Hardy inequality to arbitrary integer orders to establish optimal discrete -Rellich and -Birman inequalities, utilizing a novel Copson inequality variant with a negative exponent and demonstrating how these results recover the continuous -Birman inequality.
Motivated by recent finite-dimensional results, this paper establishes Jensen's inequality for partial traces within both semifinite and general non-tracial von Neumann algebras.
This paper establishes reverse square function estimates for functions with Fourier support near degenerate curves (for ), which are then applied to derive sharp Strichartz estimates for fractional Schrödinger equations on the one-dimensional torus and new local smoothing estimates in modulation spaces.
This paper proves the Fourier extension conjecture for the paraboloid in all dimensions greater than two by decomposing smooth Alpert projections into localized pieces and establishing a key local inequality through a bilinear approach that transforms difficult exponential sums into controllable oscillatory integrals with periodic amplitudes.
This paper classifies and analyzes exactly solvable one-dimensional complex Schrödinger operators related to the Gauss hypergeometric equation, organizing them into three geometric families (spherical, hyperbolic, and deSitterian) to compute their spectra and Green functions while establishing transmutation identities and linking them to symmetric manifolds.
This paper establishes sharp estimates for specific Littlewood-Paley square functions on , which are then used to prove the boundedness of maximal Fourier multiplier operators of Bochner-Riesz type, thereby generalizing a 1983 result by A. Carbery.
This paper establishes a new characterization of the moderate growth condition in the mixed weight matrix setting by proving its equivalence to a property of the associated weight function, thereby addressing the limitations of previous generalizations.
This paper establishes a unified framework for proving the almost everywhere pointwise convergence of sparse ergodic averages in for both deterministic and random sequences within specific parameter ranges, while providing new quantitative convergence estimates that improve upon previous non-quantitative results.
This paper introduces and analyzes convolved numbers of -sections of the Fibonacci sequence, deriving an explicit Binet-type formula for these generalized sequences and establishing their connections to Chebyshev polynomials and Lucas numbers while noting their absence from the OEIS encyclopedia.
This paper revisits Maroni's functional-analytic framework to propose a unified classification of classical orthogonal polynomials on linear lattices that recovers all known families and Bochner's original results within a single dual-topological setting, thereby correcting historical oversights where algebraically equivalent families were treated as distinct or excluded.
This paper demonstrates an asymmetry in uniqueness sets by constructing examples that fail to support measures with -summable Fourier coefficients while simultaneously supporting measures with rapidly decaying positive frequencies, thereby revealing a fundamental divergence between unilateral and bilateral uniqueness problems.
This paper characterizes the spectrum of Hausdorff operators acting on weighted Bergman and power weighted Hardy spaces defined over the upper half-plane.
This paper establishes a general sparse domination principle that respects the cancellative structure of functions across various measure spaces, including martingale and Euclidean settings, leading to new sharp weighted results for operators acting on spaces and a sparse characterization of the norm.