We develop a new and general approach to prove multiplier theorems in various geometric settings. The main idea is use martingale transforms Gundy-Varopoulos representation for multipliers defined via suitable extension procedure. Along the way, we provide probabilistic proof of generalization result by Stinga Torrea, which independent interest. Our methods here also recover sharp Lp bounds sec...

In this paper, we consider a class of stochastic pantograph differential equations with Lévy jumps (SPDEwLJs). By using the Burkholder-Davis-Gundy inequality and the Kunita’s inequality, we prove the existence and uniqueness of solutions to SPDEwLJs whose coefficients satisfying the Lipschitz conditions and the local Lipschitz conditions. Meantime, we establish the p-th exponential estimations ...

We prove that the best so far known constant cp=p−p1−p,p∈(0,1) of a domination inequality, which originates to Lenglart, is sharp. In particular, we solve an open question posed by Revuz and Yor [12]. Motivated application maximal inequalities, like e.g. Burkholder-Davis-Gundy also study inequality under additional monotonicity assumption. this special case, stays bounded for p near 1 was prove...

We show existence and uniqueness of solutions stochastic path-dependent differential equations driven by cadlag martingale noise under joint local monotonicity coercivity assumptions on the coefficients with a bound in terms supremum norm. In this set-up, usual proof using ordinary Gronwall lemma together Burkholder-Davis-Gundy inequality seems impossible. order to solve problem, we prove new q...

Abstract. We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by R. F. Gundy. By applying known results for martingales we obtain corresponding metric theore...

Objectives: The main objective of this research was an analytic assessment of Neural Tube Defects (NTDs) in pregnant women who visited Jundi Shapur university hospitals in Ahvaz from March 21, 2002 till March 20, 2004 and possible contributory factors. Methodology: This is a retrospective study from the medical documents. The results have been analytically assessed. Results: Total numbers of pr...

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