Hardy-Littlewood-Stein-Weiss type theorems for Riesz potentials and their commutators in Morrey spaces

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AYKOL KOCAKUŞAKLI C., Hasanov J. J.

STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, cilt.68, sa.3, ss.613-629, 2023 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 68 Sayı: 3
• Basım Tarihi: 2023
• Doi Numarası: 10.24193/subbmath.2023.3.11
• Dergi Adı: STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
• Sayfa Sayıları: ss.613-629
• Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider weighted Morrey spaces L-p,L-lambda,L-|& BULL; |(gamma)(R-n). We prove the Hardy-Littlewood-Stein-Weiss type L-p,lambda,|center dot|(gamma)(R-n) to L-q,lambda,|center dot|(mu)(R-n) the-orems for Riesz potential I-alpha and its commutators [b,I-alpha] and |b, I-alpha|, where 0 < alpha < n, 0 <= lambda < n -alpha, 1 < p < n-lambda/alpha , -n + lambda <= gamma < n(p - 1) + lambda, mu= q gamma/p, 1/p - 1/q = alpha/n-lambda, b is an element of BMO(R-n). As a result of these we obtain the con-ditions for the boundedness of the commutator |b, I-alpha| from Besov-Morrey spaces B-p,B-theta,lambda,|center dot|(gamma) (s)(R-n) to B-q,theta,lambda,|center dot|(mu)(s) (R-n). Furthermore, we consider the Schrodinger operator -Delta + V on R-n and obtain weighted Morrey L-p ,lambda,|center dot|(gamma)(R-n) estimates for the operators V-s(-Delta + V)(-beta) and V-s del (-Delta + V)(-beta). Finally we apply our results to various operators which are estimated from above by Riesz potentials.