NL
N. Lindemulder
Authored
14 records found
We study the pointwise multiplier property of the characteristic function of the half-space on weighted mixed-norm anisotropic vector-valued function spaces of Bessel potential and Triebel–Lizorkin type.@en
In this paper, we establish weighted Lq–Lp-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in time and in space, and yield flexibility in the opt
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In this paper, we consider traces at initial times for functions with mixed time-space smoothness. Such results are often needed in the theory of evolution equations. Our result extends and unifies many previous results. Our main improvement is that we can allow general interpola
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In this paper we consider the Laplace operator with Dirichlet boundary conditions on a smooth domain. We prove that it has a bounded H∞-calculus on weighted Lp-spaces for power weights which fall outside the classical class of Ap-weights. Furthermore, we characterize the domain o
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We prove results on complex interpolation of vector-valued Sobolev spaces over the half-line with Dirichlet boundary condition. Motivated by applications in evolution equations, the results are presented for Banach space-valued Sobolev spaces with a power weight. The proof is bas
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We prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to in
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This thesis is concerned with the maximal regularity problem for parabolic boundary value problems with inhomogeneous boundary conditions in the setting of weighted function spaces and related function space theoretic problems.
This in particularly includes weighted $L_{q}$-$L_{p
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In this paper we show that Musielak–Orlicz spaces are UMD spaces under the so-called Δ2 condition on the generalized Young function and its complemented function. We also prove that if the measure space is divisible, then a Musielak–Orlicz space has the UMD property if and only i
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We develop a discrete framework for the interpolation of Banach spaces, which contains the well-known real and complex interpolation methods, but also more recent methods like the Rademacher, γ- and ℓq-interpolation methods. Our framework is based on a sequential structure impose
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We develop a discrete framework for the interpolation of Banach spaces, which contains the well-known real and complex interpolation methods, but also more recent methods like the Rademacher, γ- and ℓq-interpolation methods. Our framework is based on a sequential structure impose
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In this paper we study elliptic and parabolic boundary value problems with inhomogeneous boundary conditions in weighted function spaces of Sobolev, Bessel potential, Besov and Triebel-Lizorkin type. As one of the main results, we solve the problem of weighted Lq-maximal regulari
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The main result of this paper is an intersection representation for a class of anisotropic vector-valued function spaces in an axiomatic setting à la Hedberg and Netrusov (2007), which includes weighted anisotropic mixed-norm Besov and Lizorkin–Triebel spaces. In the special case
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In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are RR-boundedness results for Fourier multiplier operators, which are of independent interest. As an application we characteriz
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Let E and G be two Banach function spaces, let T ∈ L(E, Y ), and let ⟨X,Y⟩ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator TY ∈ L(E(Y), G(Y )) with the property that ⟨x,Tye⟩=T⟨x,e⟩,e∈E(Y),x∈X.
The first
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