On a Closed Subspace of L^(p(.)(Ω))

Yasin Kaya

doi:10.17798/bitlisfen.651211

On a Closed Subspace of L^(p(.)(Ω))

Abstract

In this study, we first give a description of L^(p(.)(Ω)) spaces. These spaces are an important generalization of classical Lebesgue spaces. We mention their various applications in engineering and physics fields. Thereafter, as it is naturally, one of the main task in L^(p(.)(Ω)) spaces is to generalize known properties classical Lebesgue spaces L^p(Ω)) to L^(p(.)(Ω)) spaces. Provided that measure of the set Ω is finite, we extend a theorem which about a closed subspace of space, from constant exponent to variable exponent. Our proof method based on embedding between L^(p(.)(Ω)) - L^p(Ω)) spaces and the proof of constant case. The essence of the method is to take advantage of properties of Hilbert space L^2(Ω)), and also based on the use of the closed graph theorem and finite measure of the set Ω.

Keywords

Variable Exponent,Lebesgue Space,Closed Subspace

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Yasin Kaya
Türkiye

Publication Date

June 15, 2020

Submission Date

November 26, 2019

Acceptance Date

April 9, 2020

Published in Issue

Year 2020 Volume: 9 Number: 2

DOI

https://doi.org/10.17798/bitlisfen.651211

IZ

https://izlik.org/JA85FZ42WA

Cite

RIS / Bibtex

APA

Kaya, Y. (2020). On a Closed Subspace of L^(p(.)(Ω)). Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 9(2), 682-688. https://doi.org/10.17798/bitlisfen.651211

AMA

1.Kaya Y. On a Closed Subspace of L^(p(.)(Ω)). Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2020;9(2):682-688. doi:10.17798/bitlisfen.651211

Chicago

Kaya, Yasin. 2020. “On a Closed Subspace of L^(p(.)(Ω))”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 9 (2): 682-88. https://doi.org/10.17798/bitlisfen.651211.

EndNote

Kaya Y (June 1, 2020) On a Closed Subspace of L^(p(.)(Ω) . Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 9 2 682–688.

IEEE

[1]Y. Kaya, “On a Closed Subspace of L^(p(.)(Ω))”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 2, pp. 682–688, June 2020, doi: 10.17798/bitlisfen.651211.

ISNAD

Kaya, Yasin. “On a Closed Subspace of L^(p(.)(Ω))”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 9/2 (June 1, 2020): 682-688. https://doi.org/10.17798/bitlisfen.651211.

JAMA

1.Kaya Y. On a Closed Subspace of L^(p(.)(Ω)). Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2020;9:682–688.

MLA

Kaya, Yasin. “On a Closed Subspace of L^(p(.)(Ω))”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 2, June 2020, pp. 682-8, doi:10.17798/bitlisfen.651211.

Vancouver

1.Yasin Kaya. On a Closed Subspace of L^(p(.)(Ω)). Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2020 Jun. 1;9(2):682-8. doi:10.17798/bitlisfen.651211

Cited By

On Closed Subspaces of Grand Lebesgue Spaces

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi

https://doi.org/10.17798/bitlisfen.1150947