Pointwise convergence for parabolic singular integrals

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...

A pointwise estimate for the local sharp maximal function with applications to singular integrals

Following the ideas of Carleson, Garnett–Jones and Fujii, we obtain a decomposition of an arbitrary measurable function f in terms of local mean oscillations. As a main application, in the case p > n we prove a conjecture by Cruz-Uribe and Pérez about two-weight norm inequalities for singular integrals. Also we extend an inequality, due to the author, relating f and the local sharp maximal func...

Convergence of Singular Limitsfor Multi - D Semilinear Hyperbolic Systemsto Parabolic

Pointwise convergence rate for nonlinear

We introduce a new method to obtain pointwise error estimates for vanishing viscosity and nite diierence approximations of scalar conservation laws with piecewise smooth solutions. This method can deal with nitely many shocks with possible collisions. The key ingredient in our approach is an interpolation inequality between the L 1 and Lip +-bounds, which enables us to convert a global result i...

Parabolic Marcinkiewicz integrals on product spaces

‎In this paper‎, ‎we study the $L^p$ ($1