Some Basic Properties of Grand Lorentz spaces

Year 2023, , 1351 - 1360, 15.12.2023

İlker Eryılmaz , Gökhan Işık

https://doi.org/10.31466/kfbd.1272911

Abstract

The concept of Lebesgue space has been generalized to the large Lebesgue space with non-weight and weight, and the classical Lorentz space concept has been generalized to large Lorentz spaces with a similar logic. In this manuscript, it is demonstrated that there is a Banach function space that is invariant under rearrangements using the maximal function instead of normalizing the large Lorentz spaces with the rearrangement function for . In addition, coverage and inclusion properties in large Lorentz spaces are investigated.

Keywords

Distribution function, Lorentz space, grand Lorentz space

Büyük (Grand) Lorentz Uzaylarının Bazı Temel Özellikleri

Abstract

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.

Keywords

Distribution fonksiyonu, Lorentz uzayı, büyük Lorentz uzayı

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