For higher-order Riesz transforms the truncation kernel b_{k,d} is nonnegative with unit L1 norm only when k=1 or 2; for k>=3 its L1 norm tends to infinity with dimension while its Fourier transform stays bounded by 1, giving dimension-free L2 control of the truncated operator by the full one.
Verdera, The Maximal Singular Integral: Estimates in Terms of the Singular Integral , in M.A
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.CA 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
On the dimension-free control of higher order truncated Riesz transforms by higher order Riesz transforms
For higher-order Riesz transforms the truncation kernel b_{k,d} is nonnegative with unit L1 norm only when k=1 or 2; for k>=3 its L1 norm tends to infinity with dimension while its Fourier transform stays bounded by 1, giving dimension-free L2 control of the truncated operator by the full one.