On Littlewood-Paley functions
This paper is devoted to research on local properties of functions and multidimensional singular integrals in terms of their mean oscillation. The conditions guaranteeing existence of a derivative in the L p-sense at a given point are found. Spaces which remain invariant under singular integral operators are considered.
A characterization of the weighted Hardy inequality Fu 2 C F“v 2, F(0)=F’(0)=F(1)=F’(1)=0 is given.
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in is given.
Long-term behavior of concrete is modeled by several widely accepted models, such as B3, fib MC 2010, or ACI 209 whose input parameters and output values are not identical to each other. Moreover, the input and, consequently, the output values are uncertain. In this paper, fuzzy input parameters are considered in uncertainty quantification of each model response and, finally, the sets of responses are analyzed by elementary tools of evidence theory. That is, belief and plausibility functions are...