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Comp."],"abstract":"<p>We prove that for the space of functions with mixed first derivatives bounded in <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L 1\">\n  <mml:semantics>\n    <mml:msub>\n      <mml:mi>L<\/mml:mi>\n      <mml:mn>1<\/mml:mn>\n    <\/mml:msub>\n    <mml:annotation encoding=\"application\/x-tex\">L_1<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.<\/p>","DOI":"10.1090\/s0025-5718-04-01624-2","type":"journal-article","created":{"date-parts":[[2004,6,11]],"date-time":"2004-06-11T19:05:00Z","timestamp":1086980700000},"page":"1885-1901","source":"Crossref","is-referenced-by-count":35,"title":["On tractability of weighted integration over bounded and unbounded regions in \u211d^{\ud835\udd64}"],"prefix":"10.1090","volume":"73","author":[{"given":"Fred","family":"Hickernell","sequence":"first","affiliation":[]},{"given":"Ian","family":"Sloan","sequence":"additional","affiliation":[]},{"given":"Grzegorz","family":"Wasilkowski","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,1,5]]},"reference":[{"key":"1","series-title":"Lecture Notes in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0093404","volume-title":"Sequences, discrepancies and applications","volume":"1651","author":"Drmota, Michael","year":"1997","ISBN":"http:\/\/id.crossref.org\/isbn\/3540626069"},{"issue":"3","key":"2","doi-asserted-by":"publisher","first-page":"279","DOI":"10.4064\/aa96-3-7","article-title":"The inverse of the star-discrepancy depends linearly on the dimension","volume":"96","author":"Heinrich, Stefan","year":"2001","journal-title":"Acta Arith.","ISSN":"http:\/\/id.crossref.org\/issn\/0065-1036","issn-type":"print"},{"issue":"221","key":"3","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1090\/S0025-5718-98-00894-1","article-title":"A generalized discrepancy and quadrature error bound","volume":"67","author":"Hickernell, Fred J.","year":"1998","journal-title":"Math. 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