It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
In order to save CPU-time in solving large systems of equations in function spaces we decompose the large system in subsystems and solve the subsystems by an appropriate method. We give a sufficient condition for the convergence of the corresponding procedure and apply the approach to differential algebraic systems.
A convolution operator, bounded on , is bounded on , with the same operator norm, if and are conjugate exponents. It is well known that this fact is false if we replace with a general non-commutative locally compact group . In this paper we give a simple construction of a convolution operator on a suitable compact group , wich is bounded on for every and is unbounded on if .
We prove a formula relating the index of a solution and the rotation number of a certain complex vector along bifurcation diagrams.