Anisotropic maximal commutator and commutator of anisotropic maximal operator on Lorentz spaces

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Akbulut A., Isayev F. A., ŞERBETÇİ A.

Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences, cilt.44, sa.4, ss.5-12, 2024 (Scopus)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 44 Sayı: 4
• Basım Tarihi: 2024
• Dergi Adı: Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences
• Derginin Tarandığı İndeksler: Scopus
• Sayfa Sayıları: ss.5-12
• Anahtar Kelimeler: anisotropic maximal operator, BMO spaces, commutator, Lorentz spaces
• Ankara Üniversitesi Adresli: Evet

Özet

In this paper we consider the anisotropic maximal commutator Mbd and the commutator of the anisotropic maximal operator [b, Md] on the Lorentz spaces Lp,q (ℝn). We obtain necessary and sufficient conditions for the boundedness of the operators Mbd and[b, Md] on Lp,q (ℝn) when b belongs to the bounded mean oscillation space BMO(ℝn), whereby some new characterizations for certain subclasses of BMO(ℝn) are obtained.