Weighted Composition Operators Between Different Fock Spaces

Tien, Pham Trong; Khoi, Le Hai

doi:10.1007/s11118-017-9678-y

Cited by 26 publications

(18 citation statements)

References 28 publications

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“…Similarly to [17, Lemmas 2.3 and 2.4], we can easily prove the following lemmas. Lemma Let

p, q \in (0, \infty)

, let T be a linear continuous operator from

O ({boldC}^{n})

into itself and let

T : {scriptF}^{p} false(C^{n} false) \to {scriptF}^{q} false(C^{n} false)

be well‐defined.…”

Section: Preliminariesmentioning

confidence: 81%

“…As in [13, 17], the following quantities play an important role in this paper:

m_{z} false(ψ, φ false) = false| ψ (z) false| e^{\frac{{false| φ (z) false|}^{2} - {false| z false|}^{2}}{2}}, z \in {boldC}^{n}, and m false(ψ, φ false) = \underset{z \in {boldC}^{n}}{trueprefixsup} m_{z} false(ψ, φ false) .

…”

Section: Preliminariesmentioning

confidence: 99%

“…Later, Le [13] obtained much easier characterizations for the boundedness and compactness of

W_{ψ, φ}

on Hilbert Fock space

{scriptF}^{2} false(boldC false)

. Recently, in [17] the authors extended Le's results to

W_{ψ, φ}

acting from a Fock space

{scriptF}^{p} false(boldC false)

to another one

{scriptF}^{q} false(boldC false)

and stated also simpler estimates for essential norm of such operators

W_{ψ, φ}

. It should be noted that in [13, 18] the techniques of adjoint operators on Hilbert spaces played an essential role, while in the context of [17] these techniques do not work and a new approach is required.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, in [17] the authors extended Le's results to

W_{ψ, φ}

acting from a Fock space

{scriptF}^{p} false(boldC false)

to another one

{scriptF}^{q} false(boldC false)

and stated also simpler estimates for essential norm of such operators

W_{ψ, φ}

Section: Introductionmentioning

confidence: 99%

“…It should be noted that in [13, 18] the techniques of adjoint operators on Hilbert spaces played an essential role, while in the context of [17] these techniques do not work and a new approach is required. The aim of this paper is to develop the study in [17] for the case of several variables.…”

Section: Introductionmentioning

confidence: 99%

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