000			03448nam a22004935i 4500
001			978-3-0348-0548-3
003			DE-He213
005			20140220082836.0
007			cr nn 008mamaa
008			130217s2013 sz | s |||| 0|eng d
020			_a9783034805483 _9978-3-0348-0548-3
024	7		_a10.1007/978-3-0348-0548-3 _2doi
050		4	_aQA403-403.3
072		7	_aPBKD _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.785 _223
100	1		_aCruz-Uribe, David V. _eauthor.
245	1	0	_aVariable Lebesgue Spaces _h[electronic resource] : _bFoundations and Harmonic Analysis / _cby David V. Cruz-Uribe, Alberto Fiorenza.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2013.
300			_aIX, 312 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aApplied and Numerical Harmonic Analysis
505	0		_a 1 Introduction -- 2 Structure of Variable Lebesgue Spaces -- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity -- 5 Extrapolation in the Variable Lebesgue Spaces -- 6 Basic Properties of Variable Sobolev Spaces -- Appendix: Open Problems -- Bibliography -- Symbol Index -- Author Index -- Subject Index.        .
520			_aThis book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
650		0	_aMathematics.
650		0	_aHarmonic analysis.
650		0	_aFunctional analysis.
650		0	_aGlobal analysis.
650	1	4	_aMathematics.
650	2	4	_aAbstract Harmonic Analysis.
650	2	4	_aFunctional Analysis.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
700	1		_aFiorenza, Alberto. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034805476
830		0	_aApplied and Numerical Harmonic Analysis
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0548-3
912			_aZDB-2-SMA
999			_c96306 _d96306