On Some Riesz and Carleman Type Inequalities for Harmonic Functions in the Unit Disk

Kalaj, David; Bajrami, Elver

doi:10.1007/s40315-017-0226-y

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A Remark On An Isoperimetric Inequality For Harmonic Functions1

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2019

2024

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Cited by 4 publications

(2 citation statements)

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“…Remark 2.12. The proofs of the same statement for n = 2 and n = 4 can be found in [12] and in [10] respectively (where different approaches used, but applicable only for those two specific cases). The proof here works only for positive integers n ≥ 2, but probably the same estimate is true for every positive number n > 2.…”

Section: 2mentioning

confidence: 92%

On Riesz type inequalities for harmonic mappings on the unit disk

Kalaj

2019

Trans. Amer. Math. Soc.

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Section: 2mentioning

confidence: 92%

On Riesz type inequalities for harmonic mappings on the unit disk

Kalaj

2019

Trans. Amer. Math. Soc.

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“…Note that the Riesz-Thorin interpolation theorem for the Poisson extension operator gives the same estimate! For 1 < p < 2, in [24] it is proved that…”

Section: A Remark On An Isoperimetric Inequality For Harmonic Functionsmentioning

confidence: 99%

Hollenbeck-Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections

Melentijević¹

2022

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In this paper we address the problem of finding the best constants in inequalities of the form:where P + f and P − f denote analytic and co-analytic projection of a complexvalued function f ∈ L p (T), for p ≥ 2 and all s > 0, thus proving Hollenbeck-Verbitsky conjecture from [17]. We also prove the same inequalities for 1 < p ≤ 4 3 and s ≤ sec 2 π 2p and confirm that s = sec 2 π 2p is the sharp cutoff for s. The proof uses a method of plurisubharmonic minorants and an approach of proving the appropriate "elementary" inequalities that seems to be new in this topic.We show that this result implies best constants inequalities for the projections on the real-line and half-space multipliers on R n and an analog for analytic martingales. A remark on an isoperimetric inequality for harmonic functions in the unit disk is also given.

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Hollenbeck–Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections

Melentijević

2023

Math. Ann.

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On Some Riesz and Carleman Type Inequalities for Harmonic Functions in the Unit Disk

Cited by 4 publications

References 18 publications

On Riesz type inequalities for harmonic mappings on the unit disk

On Riesz type inequalities for harmonic mappings on the unit disk

Hollenbeck-Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections

Hollenbeck–Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections

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