Reel eksende değişken üslü Lebesgue uzaylarda Fejér ortalamalar

Yıl 2024, Cilt: 26 Sayı: 1, 188 - 195, 19.01.2024

Ebru Altıparmak Ali Güven

https://doi.org/10.25092/baunfbed.1356259

Öz

Değişken üslü Lebesgue uzayları klasik Lebesgue uzaylarının genellemeleridir ve Matematiksel Analizin birçok dalında öneme sahiptir. Özellikle direkt ve ters teoremler ve bunların geliştirilmesi bu uzaylarda birçok matematikçi tarafından incelenmektedir. Bu makalede, değişken üslü Lebesgue uzayı L^p(⋅) (R)'ye ait fonksiyonların Fejér ortalamalarının yakınsaklık hızına ilişkin doğrudan ve ters tahminler, uygun bir K-fonksiyonu kullanılarak oluşturulmuştur. Bu şekilde, Z. Ditzian'ın klasik Lebesgue uzaylarında L^p (R)(1

Anahtar Kelimeler

Fejer ortalamalar, Fourier dönüşüm, değişken üslü Lebesgue uzayı

Fejér means in variable exponent Lebesgue spaces on the real axis

Öz

Variable exponent Lebesgue spaces are generalizations of classical Lebesgue spaces and have importance in many branches of Mathematical Analysis. Especially, direct and converse theorems and their improvements are studied by many mathematicians in these spaces. In this article, direct and converse predictions for the rate of convergence of Fejér means of functions belonging to the variable Lebesgue space L^p(⋅) (R) are established by using an appropriate K-functional. In this way, the result of Z. Ditzian on Fejér means in classical Lebesgue spaces L^p (R)(1

Anahtar Kelimeler

Fejer means, Fourier transform, variable exponent Lebesgue space

Kaynakça

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