SHARP CONSTANTS FOR MULTIVARIATE HAUSDORFF q-INEQUALITIES

In this paper, we focus on the multivariate Hausdorff operator of the form H-Phi(f)(x) = integral((0,+infinity)n) Phi(x(1)/t(1), x(2)/t(2),...,x(n)/t(n))/t(1)t(2)...t(n) f(t(1), t(2), ...,tn)dt, where dt = dt(1) dt(2) ... dt(n) or dt = d(q)t(1) d(q)t(2) ... d(q)t(n) is the discrete measure in q-analysis. The sharp bounds for the multivariate Hausdorff operator on spaces L-p with power weights are calculated, where p is an element of R\{0}.