We suggest an elementary harmonic analysis approach to canceling and weakly differential operators, which allows us extend these notions the anisotropic setting replace operators with Fourier multiplies mild smoothness regularity. In this more general of multipliers, we prove inequality $$\|f\|_{L_\infty} \lesssim \|Af\|_{L_1}$$ if $$A$$ is a operator order $$d$$ $$\|f\|_{L_2} $$d/2$$ , provide...

‎in the present paper we investigate the $l_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time markov processes with general state‎ ‎spaces‎. ‎we provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $l_1$-weak ergodicity‎. ‎moreover‎, ‎we apply‎ ‎the obtained results to establish $l_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

We fully describe the doubly stochastic orbit of a self-adjoint element in noncommutative $$L_1$$ -space affiliated with semifinite von Neumann algebra, which answers problem posed by Alberti and Uhlmann (Stochasticity partial order: maps unitary mixing. VEB Deutscher Verlag der Wissenschaften, Berlin, 1982) 1980s, extending several results literature. It follows further from our methods that, ...

We consider the second-order asymptotic properties of‎  ‎the bootstrap of L_1 regression estimators by looking at‎ ‎the difference between the L_1 estimator and ‎its first-order approximation‎, ‎where the latter‎ ‎is the minimizer of a quadratic approximation to the‎ ‎L_1 objective function‎. ‎It is shown that the bootstrap ‎distribution of the normed difference does not converge‎ ‎(eit...

The paper deals with $$L_p$$ -boundedness of the Hartley-Fourier convolutions operator and their applied aspects. We establish various new Young-type inequalities obtain structure a normed ring in Banach space when equipping it such convolutional multiplication. Weighted -norm these are also considered. As applications, we investigate solvability bounded $$L_1$$ -solution class Fredholm-type in...

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...

Numerical study of various processes leads to the need for clarification (extensions) limits applicability computational constructs and modeling tools. In this article, we differentiability in space Lebesgue integrable functions consistency concept with fundamental constructions such as Taylor expansion finite differences is considered. The function $f$ from $L_1 [a; b]$ called $(k,L)$-differen...

The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant operators can lead to fewer measurements needed for reconstruction when employing the \(l_1\)-minimization Sensing. In this paper, we pick an eigenvector of Zauner unitary matrix and –under certain assumptions on ambient dimension– build spark deficient Gabor frame. operat...

Sufficient conditions characterizing the asymptotic stability and the hybrid L1/`1-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. The...