TY - JOUR
T1 - Sharp pointwise estimates for directional derivatives of harmonic functions in a multidimensional ball
AU - Kresin, G.
AU - Maz'ya, V.
N1 - Funding Information:
Acknowledgments. The research of the first author was supported by the KAMEA program of the Ministry of Absorption, State of Israel, and by the Ariel University Center of Samaria. The second author was partially supported by the UK Engineering and Physical Sciences Research Council grant EP/F005563/1.
PY - 2010
Y1 - 2010
N2 - A representation of the sharp constant in a pointwise estimate for the absolute value of the directional derivative of a harmonic function in a multidimensional ball is obtained under the assumption that the boundary values of the function belong to Lp. This representation is specified in the cases of radial and tangential derivatives. It is proved for p = 1 and p = 2 that the maximum of the absolute value of the directional derivative of a harmonic function with a fixed Lp-norm of its boundary values is attained at the radial direction. This confirms D. Khavinson's conjecture for p = 1 and p = 2. Bibliography: 11 titles.
AB - A representation of the sharp constant in a pointwise estimate for the absolute value of the directional derivative of a harmonic function in a multidimensional ball is obtained under the assumption that the boundary values of the function belong to Lp. This representation is specified in the cases of radial and tangential derivatives. It is proved for p = 1 and p = 2 that the maximum of the absolute value of the directional derivative of a harmonic function with a fixed Lp-norm of its boundary values is attained at the radial direction. This confirms D. Khavinson's conjecture for p = 1 and p = 2. Bibliography: 11 titles.
UR - https://www.scopus.com/pages/publications/77955842711
U2 - 10.1007/s10958-010-0045-4
DO - 10.1007/s10958-010-0045-4
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:77955842711
SN - 1072-3374
VL - 169
SP - 167
EP - 187
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
IS - 2
ER -