Geodesic
LOWER BOUNDS OF OPERATORSON WEIGHTED [Lscr]P SPACES AND LORENTZ SEQUENCE SPACES
Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 211-223

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The problem considered is thedetermination of “lower bounds” of matrix operators on the spaces\ell_p(w) or d(w,p). Under fairly general conditions, thesolution is the same for both spaces and is given by the infimum of a certain sequence. Specific casesare considered, with the weighting sequence defined by w_n = 1/n^\alpha . The exactsolution is found for the Hilbert operator. For the averaging operator, two different upper bounds aregiven, and for certain values of p and \alpha it is shown thatthe smaller of these two bounds is the exact solution. 
JAMESON, G. J. O.; LASHKARIPOUR, R. LOWER BOUNDS OF OPERATORSON WEIGHTED [Lscr]P SPACES AND LORENTZ SEQUENCE SPACES. Glasgow mathematical journal, Tome 42 (2000) no. 2, pp. 211-223. doi: 10.1017/S0017089500020061
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     author = {JAMESON, G. J. O. and LASHKARIPOUR, R.},
     title = {LOWER {BOUNDS} {OF} {OPERATORSON} {WEIGHTED} {[Lscr]P} {SPACES} {AND} {LORENTZ} {SEQUENCE} {SPACES}},
     journal = {Glasgow mathematical journal},
     pages = {211--223},
     year = {2000},
     volume = {42},
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     doi = {10.1017/S0017089500020061},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500020061/}
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