Riesz Potential and Fractional Maximal Function

In this article, we begin with Riesz potential. We then discuss some properties of the Riesz potential. Finally we discuss a relation of Riesz Potential with fractional maximal function in the sense that fractional maximal function can be controlled by Riesz potential and the fractional maximal function maps the space Lp to Lq whenever the Riesz potential does.

Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)

The smoothness of functions f in the space Lp(R) with 1<p<∞ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in Lp(R) by means of the local convergence of the semi-discrete wavelet transform.

On the convergence rate for the estimation of impulse response function in the space Lp(T)

The problem of estimation of a stochastic linear system has been a matter of active research for the last years. One of the simplest models considers a ‘black box’ with some input and a certain output. The input may be single or multiple and there is the same choice for the output. This generates a great amount of models that can be considered. The sphere of applications of these models is very extensive, ranging from signal processing and automatic control to econometrics (errors-in-variables models). In this paper a time-invariant continuous linear system is considered with a real-valued impulse response function. We assume that impulse function is square-integrable. Input signal is supposed to be Gaussian stationary stochastic process with known spectral density. A sample input–output cross-correlogram is taken as an estimator of the response function. An upper bound for the tail of the distribution of the estimation error is found that gives a convergence rate of estimator to impulse response function in the space Lp(T).

Reliability and accuracy in the space Lp(T) for the calculation of integrals depending on a parameter by the Monte Carlo method

This paper is devoted to the estimation of the accuracy and reliability (in

On some class of integral operators related to the Bergman projection

We consider the integral operator C?f(z) = ?D f(?)/(1-z?)? dA(?), z ? D, where 0 < ? < 2 and D is the unit disc in the complex plane. and investigate boundedness of it on the space Lp(D, d?), 1 < p < 1, where d? is the M?bius invariant measure in D. We also consider the spectral properties of C? when it acts on the Hilbert space L2(D, d?), i.e., in the case p = 2, when C? maps L2(D, d?) into the Dirichlet space.

On the approximation of the set of trajectories of control system described by a Volterra integral equation

In this paper, the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. It is assumed that the set of admissible control functions is the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. It is shown that the sections of the set of trajectories can be approximated by the sections of trajectories, generated by the mixed constrained and Lipschitz continuous control functions, the Lipschitz constant of which is bounded.