Some sharp inequalities for multidimensional integral operators with homogeneous kernel: an overview and new results

One goal of this paper is to point out the fact that a big number of inequalities provedfrom time to time in journal publications, both one-dimensional and multi-dimensional, are particularcases of ...

[1]  D. Hilbert.  Grundzuge Einer Allgemeinen Theorie Der Linearen Integralgleichungen , 2009 .

[2]  R. Jackson.  Inequalities , 2007, Algebra for Parents.

[3]  Lars-Erik Persson,et al.  The Prehistory of the Hardy Inequality , 2006, Am. Math. Mon..

[4]  Lars-Erik Persson,et al.  Weighted Inequalities of Hardy Type , 2003 .

[5]  S. Eilertsen.  On Weighted Fractional Integral Inequalities , 2001 .

[6]  D. Yafaev.  Sharp Constants in the Hardy–Rellich Inequalities , 1999 .

[7]  E. Stein,et al.  Introduction to Fourier analysis on Euclidean spaces (PMS-32) , 1972 .

[8]  Konrad Knopp,et al.  Über Reihen Mit Positiven Gliedern , 1928 .

[9]  J. Pečarić,et al.  Recent Advances in Hilbert-type Inequalities , 2012 .

[10]  I. Peric,et al.  Multiple Hilbert's type inequalities with a homogeneous kernel , 2011 .

[11]  N. Masmoudi.  About the Hardy Inequality , 2011 .

[12]  Lars-Erik Persson,et al.  THE HARDY INEQUALITY. ABOUT ITS HISTORY AND SOME RELATED RESULTS , 2007 .

[13]  Hong Yong.  A MULTIPLE HARDY-HILBERT'S INTEGRAL INEQUALITY WITH THE BEST CONSTANT FACTOR , 2006 .

[14]  S. Samko.  BEST CONSTANT IN THE WEIGHTED HARDY INEQUALITY: THE SPATIAL AND SPHERICAL VERSION , 2005 .

[15]  S. Samko,et al.  Equations with Involutive Operators , 2001 .

[16]  A. M. Hinz,et al.  Explicit constants for Rellich inequalities in , 1998 .

[17]  A. Kufner,et al.  Higher dimensional Hardy inequality , 1996 .

[18]  E. Stein,et al.  Fractional Integrals on n-Dimensional Euclidean Space , 1958 .

[19]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .

[20]  H. Weyl.  Singuläre integralgleichungen mit besonderer berücksichtigung des Fourierschen integraltheorems ... , 1908 .