Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

We study multivariate approximation defined over tensor product Hilbert spaces. The space is a weighted tensor product Hilbert space with exponential weights which depend on two sequences a={aj}j∈N and b={bj}j∈N of positive numbers, and on a bounded sequence of positive integers m={mj}j∈N. The sequence a is non-decreasing and the sequence b is bounded from below by a positive number. We find necessary and sufficient conditions on a,b and m to achieve the standard and new notions of tractability in the worst case setting.