No abstract

No abstract

The research about harmonic analysis associated with Jacobi expansions carried out in [1] and [3] is continued in this paper. Given the operator J (α,β) = J (α,β) − I, where J (α,β) is the three-term recurrence relation for the normalized Jacobi polynomials and I is the identity operator, we define the corresponding Littlewood-Paley-Stein g (α,β) k -functions associated with it and we prove an equivalence of norms with weights for them. As a consequence, we deduce a result for Laplace type multipliers.

We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calderón-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation operators from ℓ p (N, w) into itself, where w is a weight in the discrete Muckenhoupt class Ap(N). Moreover, we obtain weighted weak (1, 1) estimates for those operators.2010 Mathematics Subject Classification. Primary: 42C10. Secondary: 44A20.

No abstract