Inversion of a theorem on action of analytic functions and multiplicative properties of some subclasses of the hardy space H∞

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Inversion of a theorem on action of analytic functions and multiplicative properties of some subclasses of the hardy space H∞. / Vinogradov, S. A.; Petrov, A. N.

In: Journal of Mathematical Sciences, Vol. 92, No. 1, 01.01.1998, p. 3573-3588.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{966767a0233c4252a80a92ba55efa847,

title = "Inversion of a theorem on action of analytic functions and multiplicative properties of some subclasses of the hardy space H∞",

abstract = "In this paper, function spaces V ∩ lAp(ω) are considered in the context of their multiplicative structure. The space V is determined by conditions on the values of a function in a disk (for example, CA, LipAα). We denote by lA p(ω) the space of power series such that their Taylor coefficients are p-summable with weight s. For an analytic function Φ acting in a space of this type, we prove the following alternative: either Φ′(z) = 0, or the space is a Banach algebra with respect to pointwise multiplication. For a wide class of weights w, we establish the continuity of the identity embedding mult(V ∩ lAp (ω)) → mult lA p. An estimate for the lp-multiplicative norm of random polynomials is found. This estimate can be considered as an extension of the known result by Salem-Zygmund. Bibliography: 10 titles.",

author = "Vinogradov, {S. A.} and Petrov, {A. N.}",

year = "1998",

month = jan,

day = "1",

doi = "10.1007/BF02440141",

language = "English",

volume = "92",

pages = "3573--3588",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Inversion of a theorem on action of analytic functions and multiplicative properties of some subclasses of the hardy space H∞

AU - Vinogradov, S. A.

AU - Petrov, A. N.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - In this paper, function spaces V ∩ lAp(ω) are considered in the context of their multiplicative structure. The space V is determined by conditions on the values of a function in a disk (for example, CA, LipAα). We denote by lA p(ω) the space of power series such that their Taylor coefficients are p-summable with weight s. For an analytic function Φ acting in a space of this type, we prove the following alternative: either Φ′(z) = 0, or the space is a Banach algebra with respect to pointwise multiplication. For a wide class of weights w, we establish the continuity of the identity embedding mult(V ∩ lAp (ω)) → mult lA p. An estimate for the lp-multiplicative norm of random polynomials is found. This estimate can be considered as an extension of the known result by Salem-Zygmund. Bibliography: 10 titles.

AB - In this paper, function spaces V ∩ lAp(ω) are considered in the context of their multiplicative structure. The space V is determined by conditions on the values of a function in a disk (for example, CA, LipAα). We denote by lA p(ω) the space of power series such that their Taylor coefficients are p-summable with weight s. For an analytic function Φ acting in a space of this type, we prove the following alternative: either Φ′(z) = 0, or the space is a Banach algebra with respect to pointwise multiplication. For a wide class of weights w, we establish the continuity of the identity embedding mult(V ∩ lAp (ω)) → mult lA p. An estimate for the lp-multiplicative norm of random polynomials is found. This estimate can be considered as an extension of the known result by Salem-Zygmund. Bibliography: 10 titles.

UR - http://www.scopus.com/inward/record.url?scp=54749090092&partnerID=8YFLogxK

U2 - 10.1007/BF02440141

DO - 10.1007/BF02440141

M3 - Article

AN - SCOPUS:54749090092

VL - 92

SP - 3573

EP - 3588

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 27078637