TY - JOUR

T1 - Complex symmetric Toeplitz operators on the generalized derivative Hardy space

AU - Ko, Eungil

AU - Lee, Ji Eun

AU - Lee, Jongrak

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2022

Y1 - 2022

N2 - The generalized derivative Hardy space Sα,β2(D) consists of all functions whose derivatives are in the Hardy and Bergman spaces as follows: for positive integers α, β, Sα,β2(D)={f∈H(D):∥f∥Sα,β22=∥f∥H22+α+βαβ∥f′∥A22+1αβ∥f′∥H22<∞}, where H(D) denotes the space of all functions analytic on the open unit disk D. In this paper, we study characterizations for Toeplitz operators to be complex symmetric on the generalized derivative Hardy space Sα,β2(D) with respect to some conjugations Cξ, Cμ,λ. Moreover, for any conjugation C, we consider the necessary and sufficient conditions for complex symmetric Toeplitz operators with the symbol φ of the form φ(z)=∑n=1∞φˆ(−n)‾z‾n+∑n=0∞φˆ(n)zn. Next, we also study complex symmetric Toeplitz operators with non-harmonic symbols on the generalized derivative Hardy space Sα,β2(D).

AB - The generalized derivative Hardy space Sα,β2(D) consists of all functions whose derivatives are in the Hardy and Bergman spaces as follows: for positive integers α, β, Sα,β2(D)={f∈H(D):∥f∥Sα,β22=∥f∥H22+α+βαβ∥f′∥A22+1αβ∥f′∥H22<∞}, where H(D) denotes the space of all functions analytic on the open unit disk D. In this paper, we study characterizations for Toeplitz operators to be complex symmetric on the generalized derivative Hardy space Sα,β2(D) with respect to some conjugations Cξ, Cμ,λ. Moreover, for any conjugation C, we consider the necessary and sufficient conditions for complex symmetric Toeplitz operators with the symbol φ of the form φ(z)=∑n=1∞φˆ(−n)‾z‾n+∑n=0∞φˆ(n)zn. Next, we also study complex symmetric Toeplitz operators with non-harmonic symbols on the generalized derivative Hardy space Sα,β2(D).

UR - http://www.scopus.com/inward/record.url?scp=85131626925&partnerID=8YFLogxK

U2 - 10.1186/s13660-022-02810-3

DO - 10.1186/s13660-022-02810-3

M3 - Article

AN - SCOPUS:85131626925

SN - 1025-5834

VL - 2022

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

IS - 1

M1 - 74

ER -