We prove that there exists a martingale $f\in H_{p} $ f ∈ H p such that the subsequence $\{L_{2^{n}}f \}$ { L 2 n f } of Nörlund logarithmic means with respect to the Walsh system are not bounded from the martingale Hardy spaces $H_{p}$ H p to the space $weak-L_{p} $ w e a k − L p for $0< p<1 $ 0 < p < 1 . We also prove that for any $f\in L_{p}$ f ∈ L p , $p\geq 1 $ p ≥ 1 , $L_{2^{n}}f$ L 2 n f converge to f at any Lebesgue point x. Moreover, some new related inequalities are derived.

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Due to the wide usage of digital filters in communication systems, reliability and area has to be considered and deficiency tolerant channel usage are required. Throughout the decades, there are number of techniques that have been proposed to achieve fault tolerance. As the number of parallel filters are increasing in any digital device, the redundancy module should also be small in size. In this paper, a simple technique of constant multiplication reduction method is introduced in the Error Correction Codes (ECC) based parallel filters in order to reduce the size of the redundant module. Main agenda is to reduce the size of the redundant module by not affecting the functionalityof the system. The proposed scheme is coded in HDL and simulation results are obtained by using Xilinx 12.1i. The presented result shows that the slices can be reduced and hence the size. As a result of reduction in size, the optimization of area can also be concluded.

In this paper, we discuss the study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable. For applications, the suggested approach may be of interest in situations where approximation in the norm of the space is not possible. We describe the idea for the case of the abstract Cauchy problem for the evolution equation and provide more detailed example of the diffusion equation with the initial data in the nonseparable Morrey space.