caa a22 4500 445345365 CHVBK 20180317142827.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00233-011-9317-7 doi (NATIONALLICENCE)springer-10.1007/s00233-011-9317-7 Gomilko Oleksandr Nicolaus Copernicus University, Torun, Poland aut Optimal estimates for the semigroup generated by the classical Volterra operator on L p -spaces [Elektronische Daten] [Oleksandr Gomilko] Optimal upper bounds are given for the norm of the semigroup (e −tV )t≥0, where V is the classical Volterra operator acting on L p[0,1], 1≤p≤∞. In particular, for every p∈[1,∞] we prove that $$\mathop{\overline{\lim}}_{t\to+\infty}\,\left(t^{-|1/4-1/(2p)|}\|e^{-tV}\|_{L_p}\right)>0.$$ The Author(s), 2011 Volterra operator nationallicence L p -space nationallicence Operator semigroup nationallicence Semigroup Forum Springer-Verlag 83/2(2011-10-01), 343-350 0037-1912 83:2<343 2011 83 233 https://doi.org/10.1007/s00233-011-9317-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9317-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gomilko Oleksandr Nicolaus Copernicus University, Torun, Poland aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/2(2011-10-01), 343-350 0037-1912 83:2<343 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer