The metamorphic conditions and the age of thermal overprint were determined in metapelites, metaarenites and metabasites of the Tethyan Himalayan Sequence (THS) in SE Tibet using Kubler Index and vitrinite reflectance data and applying thermobarometrical (Thermocalc and PERPLEX) and geochronological methods (illite/muscovite K-Ar and zircon and apatite (U-Th)/ He chronology). The multiple folded thrust pile experienced a thermal overprint reaching locally peak conditions between the diagenetic stage (c. 170 degrees C) and the amphibolite facies (c. 600 degrees C at 10 kbar). Burial diagenesis and heating due to Early Cretaceous dyke emplacement triggered the growth of illite in the metapelites. Eocene collision-related peak metamorphic conditions have been reached at c. 44 Ma. During collision the different tectonic blocks of the THS were tectonically buried to different structural levels so that they experienced maximum greenschist to amphibolite facies metamorphism. Later, during Oligocene to Miocene times the entire THS underwent anchi- to epizonal metamorphic conditions, probably associated to continuous deformation in the flysch fold-thrust-system. This period terminated at c. 24-22 Ma. Adjacent to the north Himalayan metamorphic domes, the base of the THS was metamorphosed during Miocene times (c. 13 Ma). Post-metamorphic cooling below c. 180 degrees C lasted until Late Miocene and took place at different times.

Detrital fission-track (FT) dating can be successfully used in provenance studies of siliciclastic sediments to define the characteristic cooling ages of the source regions during erosion and sedimentation. In order to obtain more specific information about potential source regions we have developed the pebble population dating (PPD) method in which pebbles of specific lithotype are merged and dated. Dating of both zircon and apatite crystals from such pebble populations yields age distributions, which reflect the cooling ages of the given lithotype in the source area at the time of sedimentation. By this technique it is possible to define 'FT litho-terrains' in the source regions and thus outline palaeogeological maps. Two examples are presented from the Eastern Alps. (i) Comparison of FT ages from a sandstone sample and a gneiss PPD sample from an Oligocene conglomerate of the Molasse Basin shows that the youngest age cluster is present only in the sand fraction and derived from the Oligocene volcanic activity along the Periadriatic zone. The lack of the youngest ages in the gneiss pebble assemblage excludes the Oligocene exhumation of the crystalline basement from mid-crustal level. (ii) Pebble assemblages of red Bunter sandstone, gneiss and quartzite were collected from an Upper Miocene conglomerate of the Molasse Foreland Basin and merged as PPD samples. Apatite and zircon FT grain age distributions of these PPD samples, representing the largest ancient East Alpine catchment, allow generating a new combination of palaeogeological and palaeo-FT-age maps of the Eastern Alps for the Late Miocene.

We consider a vector version of Formula Not Shown -multipliers for the Dunkl transform on Formula Not Shown and we prove Formula Not Shown -inequalities for the Littlewood–Paley operators.