On a problem of zygmund

A. M. Stokolos

doi:10.1007/BF02316290

On a problem of zygmund

A. M. Stokolos

Mathematical Sciences

Odessa National University

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

2 Scopus citations

Abstract

It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.

Original language	English
Pages (from-to)	646-657
Number of pages	12
Journal	Mathematical Notes
Volume	64
Issue number	5
DOIs	https://doi.org/10.1007/BF02316290
State	Published - 1998

Scopus Subject Areas

General Mathematics

Keywords

Integrable function
Strong differentiability
The Jessen-Marcinkiewicz-Zygmund theorem
Zygmund problem

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title = "On a problem of zygmund",

abstract = " It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.",

keywords = "Integrable function, Strong differentiability, The Jessen-Marcinkiewicz-Zygmund theorem, Zygmund problem",

author = "Stokolos, \{A. M.\}",

note = "It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.",

year = "1998",

doi = "10.1007/BF02316290",

language = "English",

volume = "64",

pages = "646--657",

journal = "Mathematical Notes",

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publisher = "Pleiades Publishing",

number = "5",

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T1 - On a problem of zygmund

AU - Stokolos, A. M.

N1 - It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.

PY - 1998

Y1 - 1998

N2 - It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.

AB - It is proved that there exists an integrable function on [0, 1]2 whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable.

KW - Integrable function

KW - Strong differentiability

KW - The Jessen-Marcinkiewicz-Zygmund theorem

KW - Zygmund problem

UR - https://www.scopus.com/pages/publications/33644670564

U2 - 10.1007/BF02316290

DO - 10.1007/BF02316290

M3 - Article

SN - 0001-4346

VL - 64

SP - 646

EP - 657

JO - Mathematical Notes

JF - Mathematical Notes

IS - 5

ER -

On a problem of zygmund

Abstract

Scopus Subject Areas

Keywords

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