  Proceeding the study of local properties of analytic functions started in
[Br] we prove new dimensionless inequalities for such functions in terms of
their Chebyshev degree. As a consequence, we obtain the reverse Holder
inequalities for analytic functions with absolute (i.e., independent of
dimension) constants. For polynomials such inequalities were recently proved by
Bobkov who sharpened and generalized the previous Bourgain result and by Sodin
and Volberg.
