Sökning: "Lp space"

Visar resultat 1 - 5 av 14 avhandlingar innehållade orden Lp space.

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. Carlson type inequalities and their applications

   Författare :Leo Larsson; Viktor Burenkov; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematical analysis; Carlson’s inequality; weighted inequality; Lp space; general measure space; interpolation; embedding; Matematisk analys; Mathematical analysis; Analys; matematik; Mathematics;

   Sammanfattning : This thesis treats inequalities of Carlson type, i.e. inequalities of the form∥f∥x≤K∏i=1m∥f∥Aiθiwhere ∑i=1mθi =1 and K is some constant, independent of the function f. X and Ai are normed spaces, embedded in some Hausdorff topological vector space. LÄS MER

4. 3. Improved Lp Hardy Inequalities

   Författare :Jesper Tidblom; Ari Laptev; Andrzej Szulkin; Achilles Tertikas; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Spectral theory; Hardy inequality; MATHEMATICS; MATEMATIK;

   Sammanfattning : Paper 1 : A geometrical version of Hardy's inequality for W_0^{1,p}(D).The aim of this article is to prove a Hardy-type inequality, concerning functions in W_0^{1,p}(D) for some domain D in R^n, involving the volume of D and the distance to the boundary of D. The inequality is a generalization of a previously proved inequality by M. and T. LÄS MER

5. 4. 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

7. 5. A study of the structure and dynamics of Saturn's inner plasma disk

   Författare :Mika Holmberg; Jan-Erik Wahlund; Nikolai Piskunov; Svetlana Ratynskaia; Thomas Cravens; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Planetary magnetospheres; Saturn; magnetospheric dynamics; Saturn s inner plasma disk; ring plasma; ion densities; ion velocities; dayside nightside asymmetry; ion loss rates; Cassini; Langmuir probe; RPWS; Space Physics; Rymdfysik;

   Sammanfattning : This thesis presents a study of the inner plasma disk of Saturn. The results are derived from measurements by the instruments on board the Cassini spacecraft, mainly the Cassini Langmuir probe (LP), which has been in orbit around Saturn since 2004. LÄS MER