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$%A. Fiorenza, A summability condition on the gradient ensuring BMO, Rev. Mat. Complut. 11 (1998), no. 2, 313–324.%$

It is well-known that if , satisfies , then belongs to , the John-Nirenberg Space. We prove that this is no more true if belongs to an Orlicz space when the -function increases less than . In order to obtain , we impose a suitable uniform condition for .

1991 Mathematics Subject Classification: 46E30, 46E35.