The Social Internet of Things (SIoT) has revolutionized user experience through various applications and networking services like Health Monitoring, Assistance, Emergency Alert Systems, Collaborative Learning Platforms. However, transferring different types data between the interconnected objects in SIoT environment, including sensor data, user-generated social interaction poses challenges due ...

Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...

Consider the second order divergence form elliptic operator L with complex bounded coefficients. In general, the operators related to it (such as Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we generalize the classical approach and develop a theory of Hardy and ...

Let \begin{document}$ {\rm BMO}_{\Delta_{N}}(\mathbb{R}^{n}) $\end{document} denote a BMO space on \mathbb{R}^{n} associated to Neumann operator \mathcal{L}: = -\Delta_{N} . In this article we will show that function f\in is the trace of solution {\mathbb L}u u_{t}+ \mathcal{L} u 0, u(x, 0) f(x), where satisfies Carleson-type condition \begin{eqnarray*} \sup\limits_{x_B, r_B} r_B^{-n}\int_0^{r_...

Consider a second order divergence form elliptic operator L with complex bounded coefficients. In general, operators related to it (such as the Riesz transform or square function) lie beyond the scope of the Calderón-Zygmund theory. They need not be bounded in the classical Hardy, BMO and even some Lp spaces. In this work we develop a theory of Hardy and BMO spaces associated to L, which includ...

Abstract. In this paper, from a John-Nirenberg (JN) type inequality in BMO(R), we prove Gagliardo-Nirenberg (GN) type inequalities in Qα(R ) which mean the continuous embeddings L(R)∩Qα(R ) ⊆ L(R) for −∞ < α < β, 1/2 < β ≤ 1 and 2 ≤ r ≤ p < ∞. This result generalizes some known embeddings and implies the bilinear estimates in BMO(R) which are useful for studying Navier-Stokes equations. Meanwhi...

1,3-Butadiene (BD), a gas used widely in production and synthesis of rubber, plastics, and resins, is metabolized to three different epoxide metabolites: butadiene monoxide (BMO), butadiene bisoxide (BBO) and epoxybutanediol (ED). We have examined the role of stereochemistry in the chemical and enzyme-mediated conjugation of R- and S-BMO; RR-, SS-, and meso-BBO; and SR-, RS-, RR-, and SS-ED wit...

There are no accepted methods to grade bone marrow oedema (BMO) and fracture on magnetic resonance imaging (MRI) scans in Charcot osteoarthropathy. The aim was to devise semiquantitative BMO and fracture scores on foot and ankle MRI scans in diabetic patients with active osteoarthropathy and to assess the agreement in using these scores. Three radiologists assessed 45 scans (Siemens Avanto 1.5T...

The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...

This paper establishes the local (or global, resp.) well-posedness of the heat flow of bihharmonic maps from R to a compact Riemannian manifold without boundary for initial data with small local BMO (or BMO, resp.) norms.