New characterizations of weighted Morrey-Campanato spaces
The authors introduce and study weighted Morrey-Campanato spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n);\) here \(\alpha\in (0, \infty), q\in [1, \infty],s\) is a nonnegative integer and \(\omega\) is a Muckenhoupt weight. The classical Morrey-Campanato spaces and the weighted Morrey-Campanato spaces introduced earlier are special cases. The results obtained generalise some of the earlier results in these contexts. It is shown that the spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n)\) are all the same for different values of \(q,\) with equivalent norms. Moreover, these spaces are also equivalent to the weighted Lipschitz spaces \(\Lambda(\alpha, \omega; \mathbb{R}^n)\) introduced for all \(\alpha \in (0, \infty), q\in [1, \infty]\) and integers \(s\geq [n\alpha].\) This, in turn, is used to obtain a new characterisation of the spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n)\) for these values of the parameters.
scientific article; zbMATH DE number 5943144