The modified fractional integral operators, introduced in [4], are proved to be bounded from some Lp– space into some Lq– space with power-logarithmic weights.

Let P be a Poisson homogeneous G-space. In [Dr2], Drinfeld shows that corresponding to each p ∈ P , there is a maximal isotropic Lie subalgebra lp of the Lie algebra d, the double Lie algebra of the tangent Lie bialgebra (g, g∗) of G. Moreover, for g ∈ G, the two Lie algebras lp and lgp are related by lgp = Adg lp via the Adjoint action of G on d. In particular, they are isomorphic as Lie algeb...

In this paper we prove a sharp affine Lp Sobolev inequality for functions on R. The new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin [A2] and Talenti [T], even though it uses only the vector space structure and standard Lebesgue measure on R. For the new inequality, no inner product, norm, or conformal structure is needed at...

LetX be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem u̇(t)+ Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weighted Lp-spaces with weights ω(t) = tp(1−μ), where 1/p < μ, if and only if it has the property of maximal Lp-regularity. Moreover, it is also shown that the derivation operator D = d/dt admits anH∞-calculus in weigh...

‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(delta,gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{alpha,beta}(mathbb{R})$.

Cerebrospinal fluid (CSF) overdrainage after lumboperitoneal (LP) shunt placement for the patients with idiopathic normal pressure hydrocephalus (iNPH) is mainly caused by insufficient management of pressure settings of the shunt valve and/or siphon effect of shunt systems induced by the patient's postural changes. We here report a unique case of intracranial hypotension (IH) due to CSF leakage...

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By using the Lp(⋅)−Lp(⋅)−boundedness of a maximal operator defined on homogeneous space, it has been shown that B−B−maximal is bounded. In present paper, we aim to bring different approach boundedness generated by generalized translation under continuity assumption p(⋅)p(⋅). It noteworthy mention our weaker than uniform Hölder continuity.

Let {T (t) : t > 0} be a strongly continuous semigroup of linear contractions in Lp, 1 < p < ∞, of a σ-finite measure space. In this paper we prove that if there corresponds to each t > 0 a positive linear contraction P (t) in Lp such that |T (t)f | ≤ P (t)|f | for all f ∈ Lp, then there exists a strongly continuous semigroup {S(t) : t > 0} of positive linear contractions in Lp such that |T (t)...

We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...