We consider a porous thermoelastic body, including voidage time derivative among the independent constitutive variables. For the initial boundary value problem of such materials, we analyze the temporal behaviour of the solutions. To this aim we use the Cesaro means for the components of energy and prove the asymptotic equipartition in mean of the kinetic and strain energies.

We consider here the so called s-Carleson measures with additive logarithmic terms in the unit disc, when 0 < s < 1 and we give many equivalent definitions. As applications, we characterize the pointwise multipliers on Qs and on its logarithmic counterpart Qs,log. Boundedness of the Cesaro operator on Qs and from Qs,log to Qs is considered as well.

If the sequence a = (a„>^ E /2, i.e., ||a||2 = 2~=0 | a„ |2 < oo, define Sa as the sequence of averages 1 " 2 ak n + 1 , It follows easily from the Marcinkiewicz Interpolation Theorem that S is a bounded operator from I2 to I2; this can also be proved directly using the Cauchy-Buniakowski-Schwarz inequality [1]. S is known as the Cesàro operator. S is, of course, not bounded below, but the foll...