Generalized Riesz Potential Operator in the Modified Morrey Spaces
2nd International Conference on Mathematics and its Applications in Science and Engineering, ICMASE 2021, Salamanca, İspanya, 1 - 02 Temmuz 2021, cilt.384, ss.137-146, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 384
- Doi Numarası: 10.1007/978-3-030-96401-6_12
- Basıldığı Şehir: Salamanca
- Basıldığı Ülke: İspanya
- Sayfa Sayıları: ss.137-146
- Anahtar Kelimeler: Generalized fractional maximal operator, Generalized Riesz potential operator, Modified Morrey spaces
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet
Özet
In this paper, we prove the boundedness of generalized fractional maximal operator Mρ and generalized Riesz potential operator Iρ in the modified Morrey spaces L~p , λ(Rn). We show that the sufficient conditions for the boundedness of the operator Mρ and the operator Iρ from the modified Morrey spaces L~p , λ(Rn) to another one L~q , λ(Rn), for 1 < p< q< ∞ and from L~1 , λ(Rn) to the weak modified Morrey spaces WL~q , λ(Rn), for p= 1, 1 < q< ∞. We get the boundedness of our two-operators Iρ and Mρ in the modified Morrey spaces L~p , λ(Rn) using the local estimate given in the Lemma 2.