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...

We show that a real bounded sequence (xn) is Cesaro convergent to l if and only the of averages with indices in [αk,αk+1) converges for all α>1 . If, addition, (xn)...

In this paper, the long-time behavior of Cesaro mean fundamental solution for fractional Heat equation corresponding to random time changes in Brownian motion is studied. We consider both stable subordinators leading equations with Caputo-Djrbashian derivative and more general cases differential-convolution operators, particular, distributed order derivatives.

The class of bounded variation bvF (u, v) of fuzzy numbers introduced by [8] has been investigated further with the help of the generalized weighted mean matrix G(u, v). Imposing some restrictions on the matrix G(u, v), we have established it’s relation with different class of sequences such as our known classical sets, set of all statistically null difference sequences, Cesaro sequences etc. A...

In this study, we investigate the norm of difference operator on some sequence spaces such as Hilbert and Cesaro matrix domains. Therefore present study is a complement for those results obtained in [1].