Grand Lorentz sequence space and its multiplication operator

Oğur, Oğuz

doi:10.31801/cfsuasmas.680388

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2022

2023

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Cited by 4 publications

(1 citation statement)

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“…They studied some operators of harmonic analysis. Later, (Oğur, 2020) defined the grand Lorentz sequence spaces and studied some basic properties such as multiplication operators.…”

Section: Introductionmentioning

confidence: 99%

2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

Oğur

2022

Karadeniz Fen Bilimleri Dergisi

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“…They studied some operators of harmonic analysis. Later, (Oğur, 2020) defined the grand Lorentz sequence spaces and studied some basic properties such as multiplication operators.…”

Section: Introductionmentioning

confidence: 99%

2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

Oğur

2022

Karadeniz Fen Bilimleri Dergisi

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Büyük (Grand) Lorentz Uzaylarının Bazı Temel Özellikleri

ERYILMAZ,

IŞIK

2023

Karadeniz Fen Bilimleri Dergisi

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Lebesgue uzayı kavramı büyük Lebesgue uzayı kavramına ağırlıklı ve ağırlıksız olarak genelleştirilmiş olup klasik Lorentz uzayı kavramıda benzer mantıkla büyük Lorentz uzaylarına genelleştirilmiştir. Bu çalışmada büyük Lorentz uzaylarını yeniden düzenleme fonksiyonu ile normlandırmak yerine maksimal fonksiyon kullanarak için yeniden düzenlemeler altında değişmez olan bir Banach fonksiyon uzayı olduğu gösterilmiştir. Ayrıca büyük Lorentz uzaylarındaki kapsama özellikleri incelenmiştir.

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Multiplication Operators on Weighted Grand Lorentz Spaces with Various Properties

Eryilmaz

2023

Wseas Transactions on Mathematics

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The concept of Lebesgue space has been generalized to the grand Lebesgue space with non-weight and weight, and the classical Lorentz space concept has been generalized to grand Lorentz spaces with a similar logic. In this study, instead of using rearrangement for a measurable function, weighted Grand Lorentz spaces are defined by using the maximal function 1<=p, q<=∞ where the weight function is measurable, complex valued, and locally bounded. In addition, multiplication operators on weighted grand Lorentz spaces are defined and the fundamental properties of these operators such as boundedness, closed range, invertibility, compactness, and closedness are characterized.

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Grand Lorentz sequence space and its multiplication operator

Abstract: In this paper, we introduce the grand Lorentz sequence spaces p;q) and study on some topological properties. Also, we characterize some properties of the multiplication operator, such as compactness, Fredholmness etc., de…ned on` p;q) .

Cited by 4 publications

References 14 publications

2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

2-Normlu Büyük Dizi Uzayları Üzerine Bir Not

Büyük (Grand) Lorentz Uzaylarının Bazı Temel Özellikleri

Multiplication Operators on Weighted Grand Lorentz Spaces with Various Properties

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