Few results have been obtained on the packing spheres constant or exact formula for separable Orlicz function spaces (Yang, 2002, P.895-899, Ye, 1987, P.487-493). In this paper, by using the continuity of ideal space norm, we firstly proved that simple function class is dense in L∗ Φ function space. This is a necessary condition of interpolation theorem. Hence, the exact value of packing sphere...

We study the Lp-spectrum of the Dirac operator on complete manifolds. One of the main questions in this context is whether this spectrum depends on p. As a rst example where p-independence fails we compute explicitly the Lp-spectrum for the hyperbolic space and its product with compact spaces.

We introduce 2 parameter variants Lp,q of the Lebesgue spaces, to gain separate control on the asymptotic behaviour (p) and the local behaviour (q). Thus they behave w.r.t. p like the spaces lp and w.r.t. q like the spaces Lq on a probability space. Convolution behaves very well on those spaces.

In this note, we answer a question raised by Johnson and Schechtman [7], about the hypercontractive semigroup on {−1, 1}. More generally, we prove the theorem below. 2000 Math. Subject Classification: Primary 47D20. Seconday 47L20. In this note, we answer a question raised by Johnson and Schechtman [7]. We refer to their paper for motivation and background. In addition, we refer the reader to [...

In this paper we establish mapping properties of bilinear Coifman-Meyer multipliers acting on the product spaces H1(Rn)×bmo(Rn) and Lp(Rn)×bmo(Rn), with 1<p<∞. As application these results, obtain some related Kato-Ponce-type inequalities involving endpoint space bmo(Rn), also study pointwise a function in bmo(Rn) functions H1(Rn), h1(Rn) Lp(Rn),

A substantial amount of daylight is received by tropical countries like Malaysia. There are advantages and disadvantages to using this renewable resource in a high-rise office building. Such buildings' deep plan spaces make it difficult create uniform distribution across the space. solution for issue usage an integrated Venetian blind (VB) with horizontal light pipe (LP). Using overcast interme...

We prove that the first reduced cohomology with values in a mixing Lp-representation, 1 < p < ∞, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group has no first reduced lp-cohomology. As a byproduct, we prove a conjecture by Pansu. ...

We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on Lp(M), the non-commutative Lp-space associated with the von Neumann algebra M. For a semi-finite von Neumann algebra M, we introduce a variant of property (H), namely property HLp(M), defined in terms of orthogonal representations o...

Let ρ(x) = x− [x], χ = χ(0,1), λ(x) = χ(x) logx, and M(x) = ∑ k≤x μ(k), where μ is the Möbius function. Norms are in Lp(0,∞), 1 < p < ∞. For M1(θ) = M(1/θ) it is noted that ζ(s) ≠ 0 in s > 1/p is equivalent to ‖M1‖r < ∞ for all r ∈ (1,p). The space is the linear space generated by the functions x ρ(θ/x) with θ ∈ (0,1]. Define Gn(x)= ∫ 1 1/nM1(θ)ρ(θ/x)θ−1dθ. For all p ∈ (1,∞) we prove the two ar...

The possibility of bringing quantum gravity induced effects to the observational realm has sparkled a lot of attention recently. It is expected that the observation of high energy cosmological particles, such as photons [1] and neutrinos [2] arising from gamma ray bursts, will provide the appropriate arena to test such predictions. Also, very precise experiments already performed in atomic and ...