An $$L^1$$ L 1 -Estimate for Certain Spectral Multipliers Associated with the Ornstein–Uhlenbeck Operator

Kemppainen, Mikko

doi:10.1007/s00041-016-9459-9

Cited by 8 publications

(13 citation statements)

References 15 publications

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“…Main result. The first part of Proposition 5 refines the previous analysis of π 3 from [8], and shows that the maximal operator…”

Section: Admissible Decompositionsupporting

confidence: 79%

“…The off-diagonal estimate for 1 E tLe −tL 1 E is an immediate consequence of [8,Lemma 3] and follows by Hölder's inequality.…”

Section: Proofmentioning

confidence: 90%

“…We will consider the two statements side by side. Part I: Recall the pointwise estimate from [8,Proposition 7]:…”

Section: Non-admissible Partmentioning

confidence: 99%

“…by an immediate generalization of [8,Lemma 6]. Together with the general assumption (1) on Φ, this takes care of the first two terms of (5).…”

Section: Non-admissible Partmentioning

confidence: 99%

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Admissible decomposition for spectral multipliers on Gaussian $$L^p$$ L p

Kemppainen¹

2017

Math. Z.

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This paper concerns harmonic analysis of the Ornstein-Uhlenbeck operator L on the Euclidean space. We examine the method of decomposing a spectral multiplier φ(L) into three parts according to the notion of admissibility, which quantifies the doubling behaviour of the underlying Gaussian measure γ. We prove that the abovementioned admissible decomposition is bounded in L p (γ) for 1 < p ≤ 2 in a certain sense involving the Gaussian conical square function. The proof relates admissibility with E. Nelson's hypercontractivity theorem in a novel way.2010 Mathematics Subject Classification. 42B25 (Primary); 42B15, 42B30 (Secondary).

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“…Main result. The first part of Proposition 5 refines the previous analysis of π 3 from [8], and shows that the maximal operator…”

Section: Admissible Decompositionsupporting

confidence: 79%

“…The off-diagonal estimate for 1 E tLe −tL 1 E is an immediate consequence of [8,Lemma 3] and follows by Hölder's inequality.…”

Section: Proofmentioning

confidence: 90%

See 2 more Smart Citations

Admissible decomposition for spectral multipliers on Gaussian $$L^p$$ L p

Kemppainen¹

2017

Math. Z.

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“…Much effort [2,3,4,5,6,7,8,10,11,12,13] has gone into developing the harmonic analysis of the Ornstein-Uhlenbeck operator…”

Section: Introductionmentioning

confidence: 99%

On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup

Teuwen

2016

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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Abstract. This paper presents a closed-form expression for the integral kernels associated with the derivatives of the Ornstein-Uhlenbeck semigroup e tL . Our approach is to expand the Mehler kernel into Hermite polynomials and applying the powers L N of the Ornstein-Uhlenbeck operator to it, where we exploit the fact that the Hermite polynomials are eigenfunctions for L. As an application we give an alternative proof of the kernel estimates by [11], making all relevant quantities explicit.

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Spectral Multiplier Operators with Respect to the Gaussian Measure

Urbina-Romero

2019

Springer Monographs in Mathematics

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An $$L^1$$ L 1 -Estimate for Certain Spectral Multipliers Associated with the Ornstein–Uhlenbeck Operator

Cited by 8 publications

References 15 publications

Admissible decomposition for spectral multipliers on Gaussian $$L^p$$ L p

Admissible decomposition for spectral multipliers on Gaussian $$L^p$$ L p

On the integral kernels of derivatives of the Ornstein–Uhlenbeck semigroup

Spectral Multiplier Operators with Respect to the Gaussian Measure

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