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	American English
Journal	Mathematical Notes
Volume	64
DOIs	https://doi.org/10.1007/BF02316290
State	Published - Nov 1998

Disciplines

Mathematics

Keywords

Integrable Function
Strong Differentiability
Zygmund Problem
the Jessen-marcinkiewicz-zygmund Theorem

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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, Zygmund Problem, the Jessen-marcinkiewicz-zygmund Theorem",

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",

month = nov,

doi = "10.1007/BF02316290",

language = "American English",

volume = "64",

journal = "Mathematical Notes",

issn = "1757-7489",

publisher = "Pleiades Publishing",

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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 - 1998/11

Y1 - 1998/11

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 - Zygmund Problem

KW - the Jessen-marcinkiewicz-zygmund Theorem

UR - https://doi.org/10.1007/BF02316290

U2 - 10.1007/BF02316290

DO - 10.1007/BF02316290

M3 - Article

SN - 1757-7489

VL - 64

JO - Mathematical Notes

JF - Mathematical Notes

ER -

On a Problem of Zygmund

Abstract

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Keywords

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