doi:10.1007/s00208-019-01834-3engAlonso Gutiérrez, DavidArtstein-Avidan, ShiriGonzález Merino, BernardoJiménez, Carlos HugoVilla, RafaelRogers-Shephard and local Loomis-Whitney type inequalitiesART-2019-111669We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and obtain some new) functional versions of Rogers–Shephard type inequalities as well as some generalizations of the geometric Rogers–Shephard inequality in the case where the subspaces intersect. These generalizations can be regarded as sharp local reverse Loomis–Whitney inequalities. We also obtain a sharp local Loomis–Whitney inequality.2019http://zaguan.unizar.es/record/8850410.1007/s00208-019-01834-3http://zaguan.unizar.es/record/88504oai:zaguan.unizar.es:88504info:eu-repo/grantAgreement/ES/MINECO/MTM2015-63699-PMATHEMATISCHE ANNALEN 374, 3-4 (2019), 1719-1771All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess