We consider the equation where , () and We obtain minimal requirements to the functions and , in addition to (), under which equation () is correctly solvable in , .
In this paper the author proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with variable exponent. As an application he proved the boundedness of certain sublinear operators on the weighted variable Lebesgue space. The proof of the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent does not contain any mistakes. But in the proof of the boundedness of certain sublinear operators on the weighted...
The purpose of this note is twofold. First it is a corrigenda of our paper [RV1]. And secondly we make some remarks concerning the interpolation properties of Morrey spaces.
We prove that if K is a compact space and the space P(K × K) of regular probability measures on K × K has countable tightness in its weak* topology, then L₁(μ) is separable for every μ ∈ P(K). It has been known that such a result is a consequence of Martin's axiom MA(ω₁). Our theorem has several consequences; in particular, it generalizes a theorem due to Bourgain and Todorčević on measures on Rosenthal compacta.
By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.