BOUNDEDNESS OF SUBLINEAR OPERATORS IN HERZ-TYPE HARDY SPACES

Let p is an element of (0, 1], q is an element of (1, infinity), alpha is an element of [n(1 - 1/q), infinity) and w(1), w(2) is an element of A(1). The author proves that the norms in weighted Herz-type Hardy spaces H(K) over dot(q)(alpha,p)(w(1), w(2)) and HK(q)(alpha,p)(w(1), w(2)) can be achieved by finite central atomic decompositions in some dense subspaces of them. As an application, the author proves that if T is a sublinear operator and maps all central (alpha, q, s, w(1), w(2))(0)-atoms (resp. central (alpha, q, s, w(1), w(2))-atoms of restrict type) into uniformly bounded elements of certain quasi-Banach space B for certain nonnegative integer s no less than the integer part of alpha - n(1 - 1/q), then T uniquely extends to a bounded operator from H(K) over dot(q)(alpha,p) (w(1), w(2)) (resp. HK(q)(alpha,p) (w(1), w(2))) to B.