Whereas in stabilization of one single Lur'e system the conditions of passivity and sector boundedness for the uncertain nonlinear function in the negative feedback loop are commonly assumed, in our context of networked Lur'e systems we adopt the stronger assumptions of incremental passivity and incremental sector boundedness.
In reference [8], Grafakos considered the (L^{p} -boundedness for the maximaL^{p} -boundednessated with general measures.
Using (2.10), the boundedness of and the Lagrange's mean-value theorem for the function,,, on if or if, we have conclusion (iii).
Using these facts and the boundedness of, for the test functions, where and, we get (3.10).
Motivated by these papers, in this paper, we have the purpose to introduce some Toeplitz-type operator related to some integral operator and BMO functions, and prove the boundedness for the operator on L p spaces with variable exponent by using a sharp estimate of the operator.
We prove Lp boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, {Lαk}k, when the parameter α is greater than −1.
In this paper, the inequality of boundedness for the multilinear fractional singular integral operators associated to the weighted Lipschitz functions is estimated.
Boundedness of the estimated parameters and uniform ultimate boundedness for the tracking and observation errors are guaranteed.
Moreover, we also establish some boundedness result for the Cordoba maximal functions (Córdoba A. in Harmonic Analysis in Euclidean Spaces, pp. 29-50, 1978) associated with the Córdoba-Zygmund dilation in (mathbb{R}^{3}) with respect to some non-doubling measures.
