; TeX output 1998.06.30:1810 S;+؍Y@K`y cmr1019(+؍`-N cmbx12ICM 1998,Berlin,Aug. 18{27 =_Abstracts ofPlenaryandIn vitedLectures "V cmbx10Section: O8. Analysis`91991UUMSClassication:q42B20,42B25,11L15 W*ainger,UUStephen,UniversityUUofWisconsin,MadisonDiscreteTAnaloguesofSingularandMaximalRadonT ransforms F*oreach b> cmmi10xinRǟ^ 0er cmmi7`쭲,let 8(x;t)bGeasmoothkP-dimensionalsurfacethroughxine>Rǟ^kW.Thatis 8(x;t)isasmoGothmappingfromRǟ^` !", cmsy10%Rǟ^k dintoRǟ^`Qwith 8(x;0)Z=x.9LetJf(x)bGeafunctiononRǟ^`쭲.ThenforsuitablysmallI#wedeneUUthesingularandmaximalRadontransformsrespGectivelyas@vS f(x)=c u cmex10ZUR yO! cmsy7jtjaf( 8(x;t))K (t)dt@andy`Mf(x)=X]suph͍ٓR cmr70<<$(1շw fe z (֍jB q()j:.@cZ?z yjtjSAjf( 8(x;t))jdtY덑where[bK~isaCalderon-ZymundkernelonRǟ^kW,\andjB q()jdenotesthemea-sureoftheballofradiusinRǟ^kW.]ThefollowingisaroughstatementoftheresultUUwehaveinmindforsingularandmaximalRadontransforms. Theorem{1: $(Christ,Nagel,SteinQandW*ainger)S1andMhareloGcallybGoundeddinL^pR,hs1