Differences of Stević–Sharma operators

Wang, Shuming; Wang, Maofa; Guo, Xin

doi:10.1007/s43037-019-00051-z

Cited by 16 publications

(4 citation statements)

References 37 publications

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“…This section contains the collection of some lemmas to be used in our main results. For more details we refers [1] and [3]. Let us consider a common parameter γ for the space X defined as follows.…”

Section: Preliminariesmentioning

confidence: 99%

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Compact and order bounded sum of weighted differentiation composition operators

Sharma¹

2022

Preprint

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In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation composition operators is defined asHere H(D) is the space of all holomorphic functions on D, u = {u j } n j=0 , u j ∈ H(D), τ a holomorphic self-map of D, f (j) the jth derivative of f and weighted differentiation composition operator D j u j ,τ is defined as D j u j ,τ (f ) = u j Cτ D j (f ) = u j f (j) • τ, f ∈ H(D).

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Section: Preliminariesmentioning

confidence: 99%

“…This lemma is trivially hold for H ∞ . For the remaining proof we refer the readers [1], [13] and [14].…”

Section: Preliminariesmentioning

confidence: 99%

Compact and order bounded sum of weighted differentiation composition operators

Sharma¹

2022

Preprint

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“…In the following years, many authors studied Stevi ć-Sharma-type operators. See, for example, [26][27][28][29][30][31][32] for more investigations about these operators on the spaces of holomorphic functions in the unit disc. Stevi ć and Sharma also proposed studying their operators between spaces of holomorphic functions on the upper half-plane [33].…”

Section: Introductionmentioning

confidence: 99%

Stević–Sharma‐type operators between Bergman spaces induced by doubling weights

Du,

Li,

Liu

2024

Math Methods in App Sciences

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Using Khinchin's inequality, Geršgorin's theorem, and the atomic decomposition of Bergman spaces, we estimate the norm and essential norm of Stević–Sharma‐type operators between weighted Bergman spaces and and the sum of weighted differentiation composition operators with different symbols from the weighted Bergman spaces to . The estimates of those between Bergman spaces remove all the restrictions of a result of Stevic, Sharma, and Bhat. As a by‐product, we also get an interpolation theorem for Bergman spaces induced by doubling weights.

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“…Liu et al [22,31] studied the boundedness and compactness of T u,v,ϕ from Hardy space to the Bloch-type space or Zygmund-type space. Wang et al in [30] considered the difference of two Stević-Sharma operators and investigated its boundedness, compactness and order boundedness between Banach spaces of analytic functions. Some more related results can be found (see, e.g., [4,10,12,13,33] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Generalized Stević-Sharma type operators from derivative Hardy spaces into Zygmund-type spaces

Guo

2022

Preprint

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Let u, v be the analytic functions on the open unit disk D in the complex plane, \varphi the analytic self-map of D and m a nonnegative integer, n a positive integer that is greater than m. We consider the generalized Stevi\’{c}-Sharma type operator T_{u,v,\varphi}^{m,n}f(z)=u(z)f^{(m)}(\varphi(z))+v(z)f^{(n)}(\varphi(z)) acting from the derivative Hardy spaces into Zygmund-type spaces, and investigate its boundedness, essential norm and compactness in this paper.

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Differences of Stević–Sharma operators

Cited by 16 publications

References 37 publications

Compact and order bounded sum of weighted differentiation composition operators

Compact and order bounded sum of weighted differentiation composition operators

Stević–Sharma‐type operators between Bergman spaces induced by doubling weights

Generalized Stević-Sharma type operators from derivative Hardy spaces into Zygmund-type spaces

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