Strong and Weak Weighted Convergence of Jacobi Series

Kerman, Ron

doi:10.1006/jath.1996.3005

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Cited by 3 publications

(3 citation statements)

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“…Proof of Proposition 2.2, (i). In order to prove this property we proceed as in the proof of [22,Theorem 2]. Let 1 < p < ∞ and w ∈ A p (0, π).…”

Section: Dense Subspacesmentioning

confidence: 99%

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Variable exponent Sobolev spaces associated with Jacobi expansions

Almeida

Castro

Sanabria

et al. 2017

Journal of Mathematical Inequalities

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“…Proof of Proposition 2.2, (i). In order to prove this property we proceed as in the proof of [22,Theorem 2]. Let 1 < p < ∞ and w ∈ A p (0, π).…”

Section: Dense Subspacesmentioning

confidence: 99%

“…It is well-known ( [21]) that H is bounded from L p w (0, π) into itself. In [22,Lemma 6] it was established that S 1 and S 2 are bounded from L p w (0, π) into itself. Then, (9) implies that (10)…”

Section: Dense Subspacesmentioning

confidence: 99%

Variable exponent Sobolev spaces associated with Jacobi expansions

Almeida

Castro

Sanabria

et al. 2017

Journal of Mathematical Inequalities

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“…Indeed, let 1 < q < ∞, v a weight in the Muckenhoupt class A q (−1, 1) and F ∈ L q ((−1, 1), v). According to [32,Theorem 2] (see also the proof of [2, Proposition 2.2]), we have that…”

Section: Introductionmentioning

confidence: 99%

Discrete Harmonic Analysis Associated with Ultraspherical Expansions

2019

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In this paper we study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted p -boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated by the difference operator ∆ λ f (n) := a λ n f (n + 1) − 2f (n) + a λ n−1 f (n − 1), n ∈ N, λ > 0, where a λ n := {(2λ+n)(n+1)/[(n+λ)(n+1+λ)]} 1/2 , n ∈ N, and a λ −1 := 0. We also prove weighted p -boundedness properties of transplantation operators associated with the system {ϕ λ n } n∈N of ultraspherical functions, a family of eigenfunctions of ∆ λ . In order to show our results we previously establish a vector-valued local Calderón-Zygmund theorem in our discrete setting.

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A weighted transplantation theorem for Jacobi coefficients

Arenas

Ciaurri

Labarga

2019

Journal of Approximation Theory

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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.

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Strong and Weak Weighted Convergence of Jacobi Series

Cited by 3 publications

References 23 publications

Variable exponent Sobolev spaces associated with Jacobi expansions

Variable exponent Sobolev spaces associated with Jacobi expansions

Discrete Harmonic Analysis Associated with Ultraspherical Expansions

A weighted transplantation theorem for Jacobi coefficients

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