Tohoku Mathematical Journal
2020
June
SECOND SERIES VOL. 72, NO. 2

Tohoku Math. J.
72 (2020), 235-259

Title CALDERÓN--ZYGMUND SINGULAR INTEGRALS IN CENTRAL MORREY--ORLICZ SPACES

Author Lech Maligranda and Katsuo Matsuoka

(Received May 7, 2018, revised February 1, 2019)
Abstract. We prove the strong-type and weak-type estimates for the Calderón--Zygmund singular integrals on central Morrey--Orlicz and weak central Morrey--Orlicz spaces defined in our earlier paper [26]. Next part has similar investigations between distinct central Morrey--Orlicz and weak central Morrey--Orlicz spaces. Then we define the $\lambda$-central mean oscillation--Orlicz spaces and its weak version investigating also some estimates for a modified Calderón--Zygmund singular integrals. Also, we show boundedness of a modified Calderón--Zygmund singular integrals from central Morrey--Orlicz spaces to $\lambda$-central mean oscillation--Orlicz spaces, even for different Orlicz functions, and corresponding weak version.

Mathematics Subject Classification. Primary 46E30; Secondary 42B20, 42B35.
Key words and phrases. Calderón--Zygmund operator, Calderón--Zygmund singular integral, Orlicz function, Orlicz space, weak Orlicz space, central Morrey--Orlicz space, weak central Morrey--Orlicz space, modular inequality, $\lambda$-central mean oscillation--Orlicz space, weak $\lambda$-central mean oscillation--Orlicz space.

To the top of this page

Back to the Contents