BOUNDEDNESS OF CERTAIN BILINEAR OPERATORS ON VANISHING GENERALIZED MORREY SPACES

In this article, we consider the bilinear operator T satisfying that there exists a positive constant C-(T), depending on T, such that, for any measurable functions f and g with compact support, t is an element of R with 0 < vertical bar t vertical bar <= 1, and x is an element of R-n with 0 is not an element of supp( f (x - t . )) boolean AND supp(g(x - .)), vertical bar T(f, g)(x)vertical bar <= C-(T) integral(Rn) vertical bar f(x - ty)g(x - y)vertical bar/vertical bar y vertical bar(n) dy. We investigate the boundedness of T on the vanishing generalized Money spaces V0Lp,phi(R-n) and V infinity Lp,phi(R-n), and the boundedness of the subbilinear maximal operator M on the vanishing generalized Money space V-(*()) L-p,L-phi(R-n), and their applications to some classical (sub)bilinear operators in harmonic analysis. As a byproduct, we also show that T is bounded on generalized Morrey spaces L-p,L-phi(R-n). Some typical examples for the main results of this paper are also included.