In this paper, we establish necessary and sufficient conditions for boundedness of m-linear p-adic integral operators with general homogeneous kernel on Lebesgue spaces Morrey spaces, respectively. each case, obtain the corresponding operator norms. Also, deal some particular examples compare them previously known from literature.

Under appropriate assumptions on the $N(\Omega)$-fucntion, locally uniform Morrey estimate is presented in Musielak-Orlicz-Sobolev space. The include a new increasing condition $x$-derivative of Young complementary function $N(\Omega)$-fucntion. conclusion applies to several important nonlinear examples frequently appeared mathematical literature.

Abstract Uniqueness of Leray solutions the 3D Navier-Stokes equations is a challenging open problem. In this article we will study problem for stationary in whole space R 3 . Under some additional hypotheses, stated terms Lebesgue and Morrey spaces, show that trivial solution U ? = 0 unique solution. This type results are known as Liouville theorems.

We study embeddings between generalised Besov–Morrey spaces Nφ,p,qs(Rd). Both sufficient and necessary conditions for the are proved. Embeddings of into Lebesgue Lr(Rd) also considered. Our approach requires a wavelet characterisation which we establish system Daubechies wavelets.

BACKGROUND Comminuted radial head fractures are often associated with secondary injuries and elbow instability. OBJECTIVES The aim of this retrospective study was to evaluate how well the modular metallic radial head implant EVOLVE® prosthesis restores functional range of motion (ROM) and stability of the elbow in acute care. PATIENTS AND METHODS Eighty-five patients with comminuted radial ...

Two exact embedding theorems are proved for arbitrary interpolation functors on couples of global Morrey spaces. Since the calculation spaces is known only in certain cases, these can replace This fact demonstrated by examples real Peetre, complex Calderon’s, and a functor generated unconditionally convergent series.

We show local H\"older continuity of quasiminimizers functionals with non-standard (Musielak--Orlicz) growth. Compared previous results, we cover more general minimizing and need fewer assumptions. prove Harnack's inequality a Morrey type estimate for quasiminimizers. Combining this Ekeland's variational principle, obtain $\omega$-minimizers.

We prove that the weak Morrey space WM is contained in $$M_{{q_1}}^p$$ for 1 ≤ q1 < q p ∞. As applications, we show if commutator [b, T] bounded from Lp to Lp,∞ some ∈ (1, ∞), then b BMO, where T a Calderón-Zygmund operator. Also, ∞, BMO and only [6, M . For belonging Lipschitz class, obtain similar results.

In this paper, we establish a regularity criterion for micropolar fluid flows in terms of the one component velocity critical Morrey-Campanato space. More precisely, show that if ...&lt;?, where 0&lt;r&lt;9/10 then weak solution (u,w) is regular.

We generalize here the celebrated Partial Regularity Theory of Caffarelli, Kohn and Nirenberg to MHD equations in framework parabolic Morrey spaces. This type generalization using spaces appears be crucial when studying role pressure regularity theory for classical Navier-Stokes as well equations.