Sökning: "Banach function spaces"

Visar resultat 1 - 5 av 16 avhandlingar innehållade orden Banach function spaces.

  1. 1. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces

    Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Andrea Cianchi; Linköpings universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; Sobolev-type space; metric measure space; upper gradient; Sobolev capacity; Banach function lattice; quasi-normed space; rearrangement-invariant space; maximal operator; Lipschitz function; regularization; weak boundedness; density of Lipschitz functions; quasi-continuity; continuity; doubling measure; Poincaré inequality;

    Sammanfattning : This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. LÄS MER

  3. 2. Newtonian Spaces Based on Quasi-Banach Function Lattices

    Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Pekka Koskela; Linköpings universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; upper gradient; weak upper gradient; Banach function lattice; quasi-normed space; metric measure space;

    Sammanfattning : The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. LÄS MER

  4. 3. Interpolation of Hilbert spaces

    Författare :Yacin Ameur; Frank Hansen; Uppsala universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Interpolation; Hilbert space; K-functional; K-monotonicity; Calderon couple; Pick function; matrix monotone function; K_2-functional; Löwner s and Donoghue s theorems.; MATEMATIK; MATHEMATICS; MATEMATIK; Mathematics; Matematik;

    Sammanfattning : (i) We prove that intermediate Banach spaces A, B with respect to arbitrary Hilbert couples H, K are exact interpolation iff they are exact K-monotonic, i.e. the condition f0∊A and the inequality K(t,g0;K)≤K(t,f0;H), t>0 imply g0∊B and ||g0||B≤||f0||A (K is Peetre's K-functional). LÄS MER

  5. 4. Propagation of singularities for pseudo-differential operators and generalized Schrödinger propagators

    Författare :Karoline Johansson; Joachim Toft; Anders Olofsson; Linnéuniversitetet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Banach spaces; Fourier; Generalized time-dependent Schrödinger equation; Micro-local; Modulation spaces; Non-tangential convergence; Pseudo-differential operators; Regularity; Wave-front sets; Banachrum; Fourier; Generaliserad tidsberoende Schrödinger ekvation; Icke-tangentiell konvergens; Mikrolokal; Modulationsrum; Pseudodifferentialoperatorer; Regularitet; Vågfrontsmängder; Mathematical analysis; Analys; Mathematics; Matematik;

    Sammanfattning : In this thesis we discuss different types of regularity for distributions which appear in the theory of pseudo-differential operators and partial differential equations. Partial differential equations often appear in science and technology. LÄS MER

  7. 5. Invariant Subspaces in Spaces of Analytic Functions

    Författare :Ali Abkar; Matematik (naturvetenskapliga fakulteten); []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; functional analysis; Series; Fourier analysis; weighted Bergman space.; super-biharmonic function; quasi-Banach space of analytic functions; index; multiplier module homomorphism; multiplier; Banach space of analytic functions; hyperinvariant subspace; Serier; fourieranalys; funktionsanalys;

    Sammanfattning : Let D be a finitely connected bounded domain with smooth boundary in the complex plane. We first study Banach spaces of analytic functions on D . The main result is a theorem which converts the study of hyperinvariant subspaces on multiply connected domains into the study of hyperinvariant subspaces on domains with fewer holes. LÄS MER