Abstract Let m ∈ N m\in {\mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in Orlicz-Sobolev spaces W , φ ( mathvari...

In this paper, we define Sobolev spaces on a locally compact unimodular group in link with the spherical Fourier transform of type $\delta$. Properties these are obtained. Analogues embedding theorems proved.

We study the approximation properties of a harmonic function u ∈ H1−k(Ω), k > 0, on a relatively compact subset A of Ω, using the Generalized Finite Element Method (GFEM). If Ω = O, for a smooth, bounded domain O, we obtain that the GFEM–approximation uS ∈ S of u satisfies ‖u−uS‖H1(A) ≤ Ch‖u‖H1−k(O), where h is the typical size of the “elements” defining the GFEM–space S and γ ≥ 0 is such that ...

In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in TriebelLizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the general...

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several generalizations of formula for generalized functions polynomials. As a consequence, give new addition an integral representation these Finally, introduce family Lebesgue spaces show that some special belong to them.

‎We present a Picone's identity for the‎ ‎$mathcal{A}_{p(x)}$-Laplacian‎, ‎which is an extension of the classic‎ ‎identity for the ordinary Laplace‎. ‎Also‎, ‎some applications of our‎ ‎results in Sobolev spaces with variable exponent are suggested.

We study the approximation properties of a harmonic function u ∈ H1−k(Ω), k > 0, on relatively compact sub-domain A of Ω, using the Generalized Finite Element Method. For smooth, bounded domains Ω, we obtain that the GFEM–approximation uS satisfies ‖u−uS‖H1(A) ≤ Ch‖u‖H1−k(Ω), where h is the typical size of the “elements” defining the GFEM–space S and γ ≥ 0 is such that the local approximation s...

We investigate the steady transport equation λz + w · ∇z + az = f, λ > 0 in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions w, a are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular ...

In generalized Lebesgue spaces $L^{p(.)}$ with variable exponent $p(.)$ defined on the real axis, we obtain several inequalities of approximation by integral functions finite degree. Approximation properties Bernstein singular integrals in these are obtained. Estimates simultaneous degree proved.