Estimates for Littlewood–Paley Operators on Ball Campanato-Type Function Spaces

New John–Nirenberg–Campanato‐type spaces related to both maximal functions and their commutators

“…However, as was mentioned in Dafni et al, 14 the structure of JN p is largely a mystery and so does JN (p,q,s) 𝛼 (). For instance, even for some classical operators (such as the Hardy-Littlewood maximal operator, the Calderón-Zygmund operator, and the fractional integral), it is still unclear whether or not these operators are bounded on JN p () or JN (p,q,s) 𝛼 (); we refer the reader to earlier research 13,[16][17][18][19][20] for some related studies. The main purpose of this article is to investigate the John-Nirenberg-Campanato space from the point of view of the negative part 𝑓 − ∶= − min{𝑓 , 0} and to shed some light on the structure of John-Nirenberg-type spaces associated with both maximal functions and their commutators.…”