Theory of Function Spaces

Triebel, Hans

doi:10.1007/978-3-0346-0416-1

Cited by 2,837 publications

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“…ii) Recall that BUC k+~ = B~+~ ~ for k C Z and a ~ (0, 1), see Theorem 3.1 and (3.3). Hence Section 2.6.1 in [28] yields that 34 ~-~ MBZq A MBuck+~.…”

Section: A Fourier Multipliers and A Class Of Elliptic Symbolsmentioning

confidence: 91%

“…Here in Appendix A, we essentially follow the books of Amann [4] and Triebel [28]. Let us first remark that in this section we exclusively deal with spaces of functions and distributions over R. If ]R is replaced with R ~ we only have to modify the definition of the space A//below and all results remain true.…”

Section: A Fourier Multipliers and A Class Of Elliptic Symbolsmentioning

confidence: 99%

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Maximal regularity for a free boundary problem

Escher

Simonett

1995

NoDEA

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This paper is concerned with the motion of an incompressible fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed, impermeable layer and above by a free surface moving under the influence of gravity. The laminar flow is governed by Darey's law.We prove existence of a unique maximal classical solutipn, using methods from the theory of maximal regularity, analytic semigroups, and Fourier multipliers. Moreover, we describe a state space which can be considered as domain of parabolicity for the problem under consideration.

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“…ii) Recall that BUC k+~ = B~+~ ~ for k C Z and a ~ (0, 1), see Theorem 3.1 and (3.3). Hence Section 2.6.1 in [28] yields that 34 ~-~ MBZq A MBuck+~.…”

Section: A Fourier Multipliers and A Class Of Elliptic Symbolsmentioning

confidence: 91%

Section: A Fourier Multipliers and A Class Of Elliptic Symbolsmentioning

confidence: 99%

Maximal regularity for a free boundary problem

Escher

Simonett

1995

NoDEA

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“…Using this formula one can show that the Besov spacesḂ s pq (R d ) are independent of the choice of ψ. Also using this formula one can establish the embedding theorems, the interpolation theorems, duality, atomic decomposition and the T 1 theorems for the spacesḂ s pq (R d ); see [4,21,31,32] for more details. By Coifman's ideas, David, Journé and Semmes in [3] provided the LittlewoodPaley theory for spaces of homogeneous type introduced by Coifman and Weiss in [2].…”

Section: Introductionmentioning

confidence: 99%

Besov spaces with non-doubling measures

Deng¹,

Han

Yang

2005

Trans. Amer. Math. Soc.

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Abstract. Suppose that µ is a Radon measure on R d , which may be nondoubling. The only condition on µ is the growth condition, namely, there is a constant C 0 > 0 such that for all x ∈ supp (µ) and r > 0,where 0 < n ≤ d. In this paper, the authors establish a theory of Besov spaceṡ B s pq (µ) for 1 ≤ p, q ≤ ∞ and |s| < θ, where θ > 0 is a real number which depends on the non-doubling measure µ, C 0 , n and d. The method used to define these spaces is new even for the classical case. As applications, the lifting properties of these spaces by using the Riesz potential operators and the dual spaces are obtained.

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“…where C γ , γ > 0, is the Hölder-Zygmund space (see [ 1 ]). In the critical case k = n/p the function f ∈ W k p may not be even continuous.…”

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confidence: 99%

“…First we prove that this embedding for k ≤ n is equivalent to the continuity of the operator R k g(t) = t 0 u k/n−1 g(u)du. The case k > n is reduced to the continuity of R n by using the lifting principle [ 1 ]. Moreover, if, for example, k ≤ n, then in the supercritical case, we can replace R k by the operator of multiplication t k/n g(t).…”

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confidence: 99%