Resumen de A summability condition on the gradient ensuring BMO

Alberto Fiorenza

• It is well-known that if u Î W1,1(W), W Ì IRN satisfies ¿Du¿ Î LN (W), then u belongs to BMO (W), the John-Nirenberg Space. We prove that this is no more true if ¿Du¿ belongs to an Orlicz space LA (W) when the N-function A(t) increases less than tN. In order to obtain u Î BMO (W), we impose a suitable uniform LA condition for ¿Du¿.