Defines g_k^(α,β) Littlewood-Paley-Stein functions for the Jacobi operator J^(α,β) - I and proves weighted norm equivalence, yielding a Laplace-type multiplier theorem.
A weighted transplantation theorem for Jacobi coefficients
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abstract
We present a transplantation theorem for Jacobi coefficients in weighted spaces. In fact, by using a discrete vector-valued local Calder\'{o}n-Zygmund theory, which has recently been furnished, we prove the boundedness of transplantation operators from $\ell^p(\mathbb{N},w)$ into itself, where $w$ is a weight in the discrete Muckenhoupt class $A_{p}(\mathbb{N})$. Moreover, we obtain weighted weak $(1,1)$ estimates for those operators.
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math.CA 1years
2019 1verdicts
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Discrete Harmonic Analysis associated with Jacobi expansions III: the Littlewood-Paley-Stein $g_{k}$-functions and the Laplace type multipliers
Defines g_k^(α,β) Littlewood-Paley-Stein functions for the Jacobi operator J^(α,β) - I and proves weighted norm equivalence, yielding a Laplace-type multiplier theorem.