Integral operators in spaces of summable functions

Krasnosel’skii, M. A.; Zabreiko, P. P.; Pustylnik, Evgeniy; Sbolevskii, P. E.

doi:10.1007/978-94-010-1542-4

Cited by 406 publications

(270 citation statements)

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“…It should be noted that several of the characterisations of compactness in this section go back to [11] in the case of (commutative) L p -spaces and may be found in [16] in the case of the Haagerup L p -spaces.…”

Section: Proposition 46 Suppose That E ⊆ S(τ ) Is Strongly Symmetricmentioning

confidence: 89%

Completely positive compact operators on non-commutative symmetric spaces

Dodds

Pagter

2010

Positivity

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Section: Proposition 46 Suppose That E ⊆ S(τ ) Is Strongly Symmetricmentioning

confidence: 89%

Completely positive compact operators on non-commutative symmetric spaces

Dodds

Pagter

2010

Positivity

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“…Since the integral operator with the kernel ∇ x G(x, y), which maps L 1 (Ω) into itself, is compact (see [19]), it follows that…”

Section: Global Weak Solutions Of the Navier-stokes/fokker-planck/poimentioning

confidence: 99%

Global Weak Solutions of the Navier-Stokes / Fokker-Planck / Poisson Linked Equations

Anoshchenko¹,

Iegorov²,

Khruslov³

2014

Z. mat. fiz. anal. geom.

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We consider the initial boundary value problem for the linked NavierStokes/Fokker-Planck/Poisson equations describing the flow of a viscous incompressible fluid with highly dispersed infusion of solid charged particles which are subjected to a random impact from thermal motion of the fluid molecules. We prove the existence of global weak solutions for the problem and study some properties of these solutions.

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“…Many other authors contributed to the study of fractional powers of generators through the above integral algorithms or alternative algorithms using powers of the resolvent of H, and summaries of the subject from various aspects, at various stages of its development, with extensive references and applications, can be found in the books of Yosida [22], Friedman [9], Krasnoselskii et al [13], Triebel [20], Tanabe [19], and Pazy [16]. A comprehensive description of the subject is also given in the series of papers by Komatsu [11].…”

Section: (S S F)(x) = I Dys a (Y)(s Y F)(x) = I Dy6°(y)f(x -Y)mentioning

confidence: 99%