thisbookismainlybasedontheresultsoftheauthorandhisco-workersob-tainedinthelastfewyears.wetriedtopresentthematerialinsuchawaythatthemainideascanbeunderstoodindependentlyoftheexistingliterature.ontheotherhand,afterprovinginchapterithatthefunctionspacesintroducedviaquarkonialdecompositionscoincidewiththewell-establishedspacesb8pqandfspqwefeelfreetouseknownresultsaboutthesespaces,especiallywhenwehavenothingnewtosayabouttheassertionsused.areaderwhoismostlyinterestedinthematerialpresentedinoneofthechaptersii,iii,oriv,whicharelargelyindependentofeachother,mayskipchapteri,atthefirstglance.butmostoftherelatedproofsinthesechaptersdependsubstantiallyonthetheorydevelopedinthefirstchapter.
itisapleasuretoacknowledgethegreathelpihavereceivedfrommycol-laboratorsinjena,inparticulardorotheeharoskeandwinfriedsickel,whomadevaluablesuggestionswhichhavebeenincorporatedinthetext.iamespeciallyindebtedtodorotheeharoskeforproducingallthefiguresinthisbook.last,butnotleast,iwishtothankmyfriendandcolleaguedavidedmundsinbrightonwholookedthroughthewholemanuscriptandofferedmanycomments.