BMO SPACES, PALEY INEQUALITIES AND IDEMPO TENT MULTIPLIERS

Generalizing the classical BMO spaces defined on the unit circle T wit h vector or scalar values, we define the spaces BMOpsi q (T) and BMOps i q (T,B), where psi q (x) = e(xq) -1 for x greater than or equal to 0 and q epsilon [1, infinity[, and where B is a Banach space. Note that BMOpsi 1 (T) = BMO (T) and BMOpsi 1 (T,B) = BMO (T,B) by the John-Nir enberg theorem. Firstly, we study a generalization of the classical Pa ley inequality and improve the Blasco-Pelczynski theorem in the vector case. Secondly, we compute the idempotent multipliers of BMOpsi q (T) . Pisier conjectured that the supports of idempotent multipliers of L- psi q (T) form a Boolean algebra generated by the periodic parts and t he finite parts for 2 < q < infinity. We confirm this conjecture with L-psi q (T) replaced by BMOpsi q (T).