Elementary characterizations of generalized weighted Morrey-Campanato spaces

Let alpha is an element of (0, infinity), p, q is an element of [1, infinity), s be a nonnegative integer, and omega is an element of A(1)(R-n ) (the class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey-Campanato space L(alpha, p, q, s, omega; R-n ) and obtain its equivalence on different p is an element of [1, beta) and integers s >= left perpenticular n alpha right perpendicular (the integer part of n alpha), where beta = (1/q - alpha)(-1) when alpha < 1/q or beta = infinity when alpha >= 1/q. We then introduce the generalized weighted Lipschitz space boolean AND(alpha, q, omega; R-n ) and prove that L(alpha, p, q, s, omega; R-n ) subset of boolean AND (alpha, q, omega; R-n ) when alpha is an element of (0, infinity), s >= left perpendicular n alpha right perpendicular, and p is an element of [1, beta).