Results 11 to 20 of about 76 (75)

On a geometric combination of functions related to Prékopa–Leindler inequality

Mathematika, Volume 69, Issue 2, Page 482-507, April 2023., 2023
Abstract We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean ...
Graziano Crasta, Ilaria Fragalà
wiley   +1 more source

Quantitative Weighted Bounds for Littlewood‐Paley Functions Generated by Fractional Heat Semigroups Related with Schrödinger Operators

Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023
Let L = −Δ + V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHq(ℝn) with q > n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood ...
Li Yang, Pengtao Li, Andrea Scapellato
wiley   +1 more source

Two‐dimensional metric spheres from gluing hemispheres

Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3069-3102, December 2022., 2022
Abstract We study metric spheres (Z,dZ)$(Z, d_{Z} )$ obtained by gluing two hemispheres of S2$\mathbb {S}^{2}$ along an orientation‐preserving homeomorphism g:S1→S1$g \colon \mathbb {S}^{1} \rightarrow \mathbb {S}^{1}$, where dZ$d_{Z}$ is the canonical distance that is locally isometric to S2$\mathbb {S}^{2}$ off the seam. We show that if (Z,dZ)$(Z, d_{
Toni Ikonen
wiley   +1 more source

Littlewood–Paley Characterization for Musielak–Orlicz–Hardy Spaces Associated with Self‐Adjoint Operators

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
Let (X, d, μ) be a metric measure space endowed with a metric d and a non‐negative Borel doubling measure μ. Let L be a non‐negative self‐adjoint operator on L2(X). Assume that the (heat) kernel associated to the semigroup e−tL satisfies a Gaussian upper bound.
Jiawei Shen, Shunchao Long, Yu-long Deng, Kwok-Pun Ho   +3 more
wiley   +1 more source

Haar null and Haar meager sets: a survey and new results

Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020
Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
wiley   +1 more source

Dynamic games with (almost) perfect information

Theoretical Economics, Volume 15, Issue 2, Page 811-859, May 2020., 2020
This paper aims to solve two fundamental problems on finite‐ or infinite‐horizon dynamic games with complete information. Under some mild conditions, we prove the existence of subgame‐perfect equilibria and the upper hemicontinuity of equilibrium payoffs in general dynamic games with simultaneous moves (i.e., almost perfect information), which go ...
Wei He, Yeneng Sun
wiley   +1 more source

Egoroff’s Theorem and Lusin’s Theorem for Capacities in the Framework of g‐Expectation

Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020
In the classical real analysis theory, Egoroff’s theorem and Lusin’s theorem are two of the most important theorems. The σ‐additivity of measures plays a crucial role in the proofs of these theorems. Later, many researchers have carried out lots of studies on Egoroff’s theorem and Lusin’s theorem when the measure is monotone and nonadditive (see, e.g.,
Zhaojun Zong, Feng Hu, Xiaoxin Tian, Wenguang Yu   +3 more
wiley   +1 more source

A Note on Sobolev‐Lorentz Capacity and Hausdorff Measure

Mathematische Nachrichten, Volume 299, Issue 7, Page 1540-1548, July 2026.
ABSTRACT In this paper, we give an elementary proof that sets of zero p,1$p,1$‐Sobolev‐Lorentz capacity are Hn−p$\mathcal {H}^{n-p}$‐null sets, independently of nonlinear potential theory. We further show that there exists a set of Sobolev‐Lorentz‐(p,1)$(p,1)$ capacity equal to zero with Hausdorff dimension equal n−p$n-p$.
Daniel Campbell
wiley   +1 more source

Littlewood, Paley and almost‐orthogonality: a theory well ahead of its time

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The classic paper by Littlewood and Paley [J. Lond. Math. Soc. (1), 6 (1931), 230–233] marked the birth of Littlewood–Paley theory. We discuss this paper and its impact from a historical perspective, include an outline of the results in the paper and their subsequent significance in relation to developments over the last century, and set them ...
Anthony Carbery
wiley   +1 more source