Eveson, Simon P.; Stepanov, Vladimir D.; Ushakova, Elena P. A duality principle in weighted Sobolev spaces on the real line. (English) Zbl 1345.46028 Math. Nachr. 288, No. 8-9, 877-897 (2015). Summary: An embedding inequality of Sobolev type is characterized in the paper with the help of a duality principle and boundedness criteria for the Hardy-Steklov integral operator in weighted Lebesgue spaces. Cited in 9 Documents MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:embeddings; weighted Sobolev spaces; weighted Lebesgue spaces; duality; norm inequalities; Hardy-Steklov operator PDFBibTeX XMLCite \textit{S. P. Eveson} et al., Math. Nachr. 288, No. 8--9, 877--897 (2015; Zbl 1345.46028) Full Text: DOI References: [1] Ćurgus, Discreteness of the spectrum of second-order differential operators and associated embeddings theorems, J. Diff. Eq. 184 pp 526– (2002) · Zbl 1029.34070 [2] Gogatishvili, The generalized Hardy operators with kernel and variable integral limits in Banach function spaces, J. Inequal. Appl. 4 pp 1– (1999) · Zbl 0947.47020 [3] Heinig, Mapping properties of integral averaging operators, Studia Math. 129 pp 157– (1998) [4] Maz’ya, On certain integral inequalities for functions of many variables, Problems of Mathematical Analysis 3 pp 33– (1972) [5] Maz’ya, Sobolev Spaces (1985) [6] Maz’ya, Conductor inequalities and criteria for Sobolev type two-weight imbeddings, J. Comput. Appl. Math. 194 (1) pp 94– (2006) · Zbl 1104.46020 [7] Mynbaev, Weighted Function Spaces and the Spectrum of Differential Operators (Russian) (1988) · Zbl 0651.46037 [8] Oinarov, On weighted norm inequalities with three weights, J. London Math. Soc. 48 pp 103– (1993) · Zbl 0811.26008 [9] Oinarov, A weighted estimate for an intermediate operator on the cone of nonnegative functions, Siberian Math. J. 43 (128-139) pp 128– (2002) [10] Oinarov, Reversion of Hölder type inequalities for sums of weighted norms and additive weighted estimates of integral operators, Math. Inequal. Appl. 6 pp 421– (2003) · Zbl 1044.26009 [11] Oinarov, Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space, Complex Var. Elliptic Eq. 56 pp 1021– (2011) · Zbl 1226.26013 [12] Oinarov, A criterion for the discreteness of the spectrum of the general Sturm-Liouville operator and embedding theorems connected with it, Diff. Eqs. 24 pp 402– (1988) [13] Prokhorov, Inequalities with measures of Sobolev embedding theorems type on open sets of the real axis, Siberian Math. J. 43 pp 694– (2002) · Zbl 1053.46021 [14] Sinnamon, The weighted Hardy inequality: new proofs and the case p=1, J. London Math. Soc. 54 pp 89– (1996) · Zbl 0856.26012 [15] Stepanov, On integral operators with variable limits of integration, Proc. Steklov Inst. Math. 232 pp 290– (2001) · Zbl 1007.46036 [16] Stepanov, Hardy operator with variable limits on monotone functions, J. Funct. Spaces Appl. 1 pp 1– (2003) · Zbl 1063.26020 [17] Stepanov, On the geometric mean operator with variable limits of integration, Proc. Steklov Inst. Math. 260 pp 264– (2008) · Zbl 1233.42001 [18] Stepanov, On boundedness of a certain class of Hardy-Steklov type operators in Lebesgue spaces, Banach J. Math. Anal. 4 pp 28– (2010) · Zbl 1193.26013 [19] Stepanov, Kernel operators with variable intervals of integration in Lebesgue spaces and applications, Math. Ineq. Appl. 13 pp 449– (2010) · Zbl 1190.26012 [20] Ushakova, On boundedness and compactness of a certain class of kernel operators, J. Funct. Spaces Appl. 9 pp 67– (2011) · Zbl 1250.47032 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.