Abstract In this paper endpoint entropy Fefferman–Stein bounds for Calderón–Zygmund operators introduced by Rahm (J Math Anal Appl 504(1):Paper No. 125372, 2021) are extended to iterated Coifman–Rochberg–Weiss commutators.

In this paper, we study the controllability of a coupled first-order hyperbolic-elliptic system in interval $ (0, 1) by Dirichlet boundary control acting at left endpoint hyperbolic component only. Using multiplier approach and compactness-uniqueness argument, establish exact for model, any time T>1 $. We explore method moments to conclude critical T = 1 For case small time, that is T<1 $...

the aim of the paper is to analyze electro-thermo nonlinear vibration of a double-piezoelectric composite microplate-system (dpcmps) based on nonlocal piezoelasticity theory. the two microplates are assumed to be connected by an enclosing elastic medium which is simulated by pasternak foundation. both of smart composite microplates are made of poly-vinylidene fluoride (pvdf) reinforced by zigza...