STRONG VARIATIONAL AND JUMP INEQUALITIES IN HARMONIC ANALYSIS 1. Introduction
Variational and jump inequalities in probability, Page 1 TRANSACTIONS OF THE AMERICAN …

We extend the sharp weighted bound of the A2 theorem to the q‐variation norm of certain
Calderón–Zygmund operators (q> 2), a stronger nonlinearity than the maximal truncations …

Weighted variation inequalities for differential operators and singular integrals in higher
dimensions Page 1 SCIENCE CHINA Mathematics CrossMark August 2017 Vol.60 No.8 …

We establish the map** properties of the singular integral operators, the Fourier integral
operators and the geometric maximal operators on the Orlicz-slice spaces by using …

We prove weighted strong q-variation inequalities with 2< q<∞ for differential and singular
integral operators. For the first family of operators the weights used can be either Sawyer's …

In this paper we establish dimension free L p (ℝ n,| x| α) norm inequalities (1< p<∞) for the
oscillation and variation of the Riesz transforms in ℝ n. In doing so we find A p-weighted …

In this paper, we systematically study jump and variational inequalities for rough operators,
whose research have been initiated by Jones et al. More precisely, we show some jump and …

In this paper, we establish\mathcal B B-valued variational inequalities for differential
operators, ergodic averages and symmetric diffusion semigroups under the condition that …

Abstract Let λ∈(-1 2,∞), and {W t λ} t> 0 be the heat semigroup related to the Bessel
Schrödinger operator S λ:=-d 2 dx 2+ λ 2-λ x 2 on R+:=(0,∞). The authors introduce the …

Let p∈(1,∞), ρ∈(2,∞) and W be a matrix A p weight. In this paper, we introduce a version of
variation 𝒱 ρ (𝒯 n,∗) for matrix Calderón–Zygmund operators with modulus of continuity …