. "1"^^ . . . "Sou\u010Dasn\u00E1 teorie prostor\u016F funkc\u00ED a aplikace" . "2012-12-31+01:00"^^ . "0"^^ . . . "11"^^ . . "11"^^ . . . . "The project was concerned with an interesting area. The team obtained new valuable results. The data in the final card are adequate. The obtained results are important for several areas of mathematics. The results are contained in 11 papers sent to impacted journals: 4 published, 2 accepted 5 are in reviewing process."@en . . . " extrapolation" . "2014-01-30+01:00"^^ . " theorems" . . . " analysis" . "Contemporary function spaces theory and applications"@en . . " Navier-Stokes" . . . "GAP201/10/1920" . . . "This project can be briefly\u00A0characterized as investigation of imbedding and trace properties of weighted and anisotropic spaces of Sobolev type, research in the extrapolation theory, and applications to the qualitative theory of differential equations, particularly to the Stokes and Oseen problem and also to the Navier-Stokes systems. Specifically we intend to study imbeddings, traces ad interpolation inequalities\u00A0in general spaces of Besov and Lizorkin-Triebel type with dominating mixed smoothness\u00A0in the framework of the Fourier analytic approach to the theory, and some of the related unsolved problems not falling into this general scheme as reduced imbeddings and inequalities in Orlicz spaces. Application areas include weighted estimates for the heat kernel, shape optimization and properties of very weak solutions to Navier-Stokes problems in weighted spaces and various type of domains."@en . "http://www.isvav.cz/projectDetail.do?rowId=GAP201/10/1920"^^ . " imbedding" . "Projekt se zab\u00FDval zaj\u00EDmavou problematikou a byly z\u00EDsk\u00E1ny nov\u00E9 cenn\u00E9 v\u00FDsledky. \u00DAdaje uveden\u00E9 v z\u00E1v\u011Bre\u010Dn\u00E9 kart\u011B jsou adekv\u00E1tn\u00ED a vystihuj\u00ED dosa\u017Een\u00E9 v\u00FDsledky. Z\u00EDskan\u00E9 v\u00FDsledky jsou d\u016Fle\u017Eitou pro n\u011Bkolik dal\u0161\u00EDch parti\u00ED matematiky. V\u00FDsledky projektu jsou obsa\u017Een\u00E9 v 11 prac\u00EDch zaslan\u00FDch do impaktovan\u00FDch \u010Dasopis\u016F. 4 pr\u00E1ce byly uve\u0159ejn\u011Bny, 2 byly k publikaci p\u0159ijaty, zbyl\u00E9 jsou v recenzn\u00EDm \u0159\u00EDzen\u00ED."@cs . "function" . "function; spaces; Fourier; analysis; imbedding; theorems; extrapolation; Navier-Stokes; equations"@en . "Tento projekt lze stru\u010Dn\u011B\u00A0charakterizovat jako studium vlastnost\u00ED vno\u0159en\u00ED a stop\u00A0v\u00E1hov\u00FDch a anizotropn\u00EDch prostor\u016F Sobolevova typu, v\u00FDzkum v oblasti teorie extrapolac\u00ED a aplikace v kvalitativn\u00ED teorii diferenci\u00E1ln\u00EDch rovnic, speci\u00E1ln\u011B t\u00FDkaj\u00EDc\u00ED se Stokesova a Oseenova probl\u00E9mu v mechanice tekutin a rovn\u011B\u017E Navierov\u00FDch-Stokesov\u00FDch syst\u00E9m\u016F. Konkr\u00E9tn\u011B pl\u00E1nujeme\u00A0studium vno\u0159en\u00ED a interpola\u010Dn\u00EDch nerovnost\u00ED v obecn\u00FDch\u00A0prostorech B\u011Bsovova a\u00A0Lizorkinova-Triebelova typu s dominuj\u00EDc\u00EDmi sm\u00ED\u0161en\u00FDmi derivacemi\u00A0v r\u00E1mci\u00A0fourierovsk\u00E9ho p\u0159\u00EDstupu k teorii a studium n\u011Bkter\u00FDch\u00A0p\u0159\u00EDbuzn\u00FDch ne\u0159e\u0161en\u00FDch probl\u00E9m\u016F v prostorech nespadaj\u00EDc\u00EDch pod obecnou fourierovskou teorii\u00A0jako redukovan\u00E1 vno\u0159en\u00ED a nerovnosti v\u00A0Orliczov\u00FDch prostorech. Oblasti aplikac\u00ED zahrnou\u00A0v\u00E1hov\u00E9 odhady pro tepeln\u00E9 j\u00E1dro, tvarovou optimalizaci\u00A0a vlastnosti velmi slab\u00FDch \u0159e\u0161en\u00ED\u00A0Navierov\u00FDch-Stokesov\u00FDch probl\u00E9m\u016F ve v\u00E1hov\u00FDch prostorech a r\u016Fzn\u00FDch typech oblast\u00ED." . "2010-01-01+01:00"^^ . " Fourier" . . "2012-03-30+02:00"^^ . "0"^^ . " spaces" .