Sharp Riesz-Fejér Inequality for Harmonic Hardy Spaces

Melentijević, Petar; Božin, Vladimir

doi:10.1007/s11118-020-09839-3

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A Remark On An Isoperimetric Inequality For Harmonic Functions1

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2023

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Cited by 6 publications

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“…We will prove this inequality with constant C p better than that in [20], following the approach from [29], where the problem earlier considered in [22] is completely solved. In [13], the authors considered similar problem in half-space setting using variational approach.…”

Section: A Remark On An Isoperimetric Inequality For Harmonic Functionsmentioning

confidence: 91%

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

Melentijević¹

2022

Preprint

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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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Section: A Remark On An Isoperimetric Inequality For Harmonic Functionsmentioning

confidence: 91%

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

Melentijević¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

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

Melentijević

2023

Math. Ann.

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On (Fejér-)Riesz type inequalities, Hardy–Littlewood type theorems and smooth moduli

Chen,

Hamada

2023

Math. Z.

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Sharp Riesz-Fejér Inequality for Harmonic Hardy Spaces

Abstract: We prove sharp version of Riesz-Fejér inequality for functions in harmonic Hardy space h p (D) on the unit disk D, for p > 1, thus extending the result from [9] and resolving the posed conjecture.2010 Mathematics Subject Classification. Primary 31A05, Secondary 30H10.

Cited by 6 publications

References 11 publications

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

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

On (Fejér-)Riesz type inequalities, Hardy–Littlewood type theorems and smooth moduli

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