Let (0, ) and := -d 2 dx 2 -2+1 x d dx be the Bessel operator on R + := (0, ).In this paper, we study some embeddings into the total Morrey space L p,, (R + , dm ), 0 , < 2 + 2 associated with the Bessel operator on R + .These spaces generalize the Morrey space associated with the Bessel operator on R + so that L p, (R + , dm ) L p,, (R + , dm ) and the modified Morrey spaces associated with the Bessel operator on R + so that L p, (R + , dm ) L p,,0 (R + , dm ).

In the framework of rational Dunkl analysis on the real line, we introduce Dunkl-type Besov-Fofana spaces which include Besov-Dunkl spaces and Dunkl-type Besov-Morrey spaces.As applications, we establish the boundedness of Dunkl-type fractional integral and fractional maximal operators in these spaces.

In this paper are proved the strong law of large numbers and the central limit theorem for the Markov random walks describes by the generalization autoregressive process of order one.

In this work, we consider a transmission problem for an elastic-thermoelastic bar with the elastic part being surrounded by two thermoelastic parts in the presence of an infinite distributed delay term.The heat flux of the system is governed by Cattaneo's law.Under suitable assumption on the weight of the delay, we establish the polynomial stability of the solution by introducing a suitable Lyapunov functional.

We study the boundedness of the commutators of Marcinkiewicz operators µ Ω,b with rough kernels Ω ∈ Ls(S n-1 ) for some s ∈ (1, ∞] and BM O function b on generalized weighted Morrey spaces Mp,ϕ(w).In the case of b ∈ BM O(R n ) we find the sufficient conditions on the pair (ϕ 1 , ϕ 2 ) with s < p < ∞ and w ∈ A p/s or 1 < p < s and w 1-p ∈ A p /s which ensures the boundedness of the operators µ Ω,b from one generalized weighted Morrey space Mp,ϕ 1 (w) to another Mp,ϕ 2 (w).