Sharp norm estimates for composition operators and Hilbert-type inequalities

Brevig, Ole Fredrik

doi:10.1112/blms.12092

Cited by 14 publications

(11 citation statements)

References 12 publications

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“…Finally, the boundedness and norm of the corresponding series operator and integral operator are discussed. The relevant literature can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Preliminariesmentioning

confidence: 99%

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Chen

et al. 2020

Journal of Function Spaces

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Let Gu,v be a homogeneous nonnegative function of order λ,Kn,xm,ρ=Gnλ1,xm,ρλ2. By using the weight coefficient method, the equivalent parameter conditions and best constant factors for the validity of the following half-discrete Hilbert-type multiple integral inequality ∫ℝ+m ∑n=1∞ Kn,xm,ρanfxdx≤Ma~p,αfq,β are discussed. Finally, its applications in operator theory are discussed.

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Section: Preliminariesmentioning

confidence: 99%

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Chen

et al. 2020

Journal of Function Spaces

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“…We know from [BB19, Theorem 3] that C ϕ is bounded on H p if and only if the local embedding (4.3) holds. We note in passing that if p is an even integer or p = ∞, then actually C ϕ H p →H p = 2 1/p by results in [Bre17] and [QQ21,Section 8.11].…”

Section: H P (T ∞ ) and Applications To Hardy Spaces Of Dirichlet Seriesmentioning

confidence: 84%

Idempotent Fourier multipliers acting contractively on $$H^p$$ spaces

2021

Self Cite

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We describe the idempotent Fourier multipliers that act contractively on $$H^p$$ H p spaces of the d-dimensional torus $$\mathbb {T}^d$$ T d for $$d\ge 1$$ d ≥ 1 and $$1\le p \le \infty $$ 1 ≤ p ≤ ∞ . When p is not an even integer, such multipliers are just restrictions of contractive idempotent multipliers on $$L^p$$ L p spaces, which in turn can be described by suitably combining results of Rudin and Andô. When $$p=2(n+1)$$ p = 2 ( n + 1 ) , with n a positive integer, contractivity depends in an interesting geometric way on n, d, and the dimension of the set of frequencies associated with the multiplier. Our results allow us to construct a linear operator that is densely defined on $$H^p(\mathbb {T}^\infty )$$ H p ( T ∞ ) for every $$1 \le p \le \infty $$ 1 ≤ p ≤ ∞ and that extends to a bounded operator if and only if $$p=2,4,\ldots ,2(n+1)$$ p = 2 , 4 , … , 2 ( n + 1 ) .

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“…To our knowledge, except the recent work of Brevig [4] in a slightly different context, no result has appeared in the literature on sharp evaluations of the norm of C ϕ when c 0 = 0. The purpose of this work is to make some attempt, in the apparently simple-minded case…”

Section: A Special But Interesting Casementioning

confidence: 98%

Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space

Muthukumar

Ponnusamy

Queffélec

2018

Integr. Equ. Oper. Theory

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By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on H 2 , the space of Dirichlet series with square summable coefficients, for the inducing symbol ϕ(s) = c1 + cqq −s where q ≥ 2 is a fixed integer. We also give an estimate on the approximation numbers of such an operator.Mathematics Subject Classification (2010). Primary: 47B33, 47B38; Secondary: 11M36, 37C30.

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Sharp norm estimates for composition operators and Hilbert-type inequalities

Cited by 14 publications

References 12 publications

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Equivalent Parameter Conditions for the Validity of Half-Discrete Hilbert-Type Multiple Integral Inequality with Generalized Homogeneous Kernel

Idempotent Fourier multipliers acting contractively on $$H^p$$ spaces

Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space

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