Factorization of Cesàro operator and related inequalities

In this paper, we introduce two factorizations for the Cesàro matrix of order n based on Cesàro and gamma matrices. The results of these factorizations are new inequalities, one of which is a generalized version of the well-known Hardy’s inequality. Moreover, we obtain the norm of Cesàro operator of order n on Cesàro and gamma matrix domains.

Generalized Hausdorff Operators on K ̇ α , q β , p ℝ and H K ̇ α , q β , p , N ℝ in the Dunkl Settings

In the present paper, we obtain some new results, and we generalize some known results for the Hausdorff operators. We have studied the generalized Hausdorff operators H α , φ on the Dunkl-type homogeneous weighted Herz spaces K ̇ α , q β , p ℝ and Dunkl Herz-type Hardy spaces H K ̇ α , q β , p , N ℝ . We have determined simple sufficient conditions for these operators to be bounded on these spaces. As applications, we provide necessary and sufficient conditions for generalized Cesàro operator to be bounded on K ̇ α , q β , p ℝ and Hardy inequality for K ̇ α , q β , p ℝ .

The Cesàro Operator on Some Sequence Spaces in Riesz Space of Non-Absolute Type

The Cesàro operators are investigated on the class -valued sequence spaces , and with is a Riesz space. Besides, we also carry out that are order bounded operators.

The trace of the commutator of the Cesàro operator and a compact operator

In this note we will prove that the trace of a commutator of the discrete Cesáro operator and a compact operator is zero when the commutator belongs to the trace-class.