engleski

H–distributions: an extension of H-measures

H--measures were introduced by Luc Tartar (1990), and independently by Patrick G\'erard (under the name of microlocal defect measures, 1991), and proved to be a powerful tool for treating weakly converging sequences of solutions to partial differential equations. Recently, a number of variants has been introduced (see the introduction in \cite{; ; ; AL}; ; ; ). \\ However, H--measures are essentially adapted to the ${; ; ; \rm L}; ; ; ^2$ framework, and we proposed \cite{; ; ; AM}; ; ; an extension which can also treat the ${; ; ; \rm L}; ; ; ^p - {; ; ; \rm L}; ; ; ^q$ pairing. The proof of their existence is based on the classical multiplier theorems. \\ The general framework for construction of variant H--measures and analogous objects will be discussed, together with some recent extensions and applications \cite{; ; ; LM, AAP, MM}; ; ; . \bibitem{; ; ; AM}; ; ; Antoni\'c, N. and Mitrovi\'c, D., {; ; ; \textit {; ; ; H--distributions: an extension of H--measures to ${; ; ; \rm L}; ; ; ^p - {; ; ; \rm L}; ; ; ^q$ setting}; ; ; }; ; ; , Abs.~Appl.~Analysis, {; ; ; \bf 2011}; ; ; , Article ID 901084, 12 pages (2011). \bibitem{; ; ; LM}; ; ; Lazar, M. and Mitrovi\'c, D., {; ; ; \textit {; ; ; On an extension of a bilinear functional on ${; ; ; \rm L}; ; ; ^p({; ; ; \bf R}; ; ; ^d)\otimes E$ to a B\^ochner space with an application to velocity averaging}; ; ; }; ; ; , Comptes Rendus Math., {; ; ; \bf 351}; ; ; 261--264 (2013). \bibitem{; ; ; AL}; ; ; Antoni\'c, N. and Lazar, M., {; ; ; \textit {; ; ; Parabolic H--measures}; ; ; }; ; ; , J. Functional Analysis, in press, 50 pages (2013). \bibitem{; ; ; AAP}; ; ; Aleksi\'c, J., Antoni\'c, N. and Pilipovi\'c, S., {; ; ; \textit {; ; ; H--distributions via weighted spaces of distributions}; ; ; }; ; ; , submitted (2013). \bibitem{; ; ; MM}; ; ; Mi\v{; ; ; s}; ; ; ur, M. and Mitrovi\'c, D., {; ; ; \textit {; ; ; On a generalisation of compensated compactness in the ${; ; ; \rm L}; ; ; ^p - {; ; ; \rm L}; ; ; ^q$ setting}; ; ; }; ; ; , submitted (2013).

H-measure ; H-distribution

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