TY - JOUR

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

AU - Ko, Eungil

AU - Lee, Ji Eun

AU - Lee, Jongrak

N1 - Funding Information:
The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIT) (2019R1F1A1058633) and this research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2019R1A6A1A11051177). The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT)(2019R1A2C1002653). The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2021R1C1C11008713).
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

VL - 2022

JO - Journal of Inequalities and Applications

JF - Journal of Inequalities and Applications

SN - 1025-5834

IS - 1

M1 - 74

ER -