Sentence examples for commutator is defined from inspiring English sources

For a suitable function f, the commutator is defined by ([b,T]f=bT f -T(bf)).

If X and Y are column vectors of operators, the commutator is defined by ([X,Y^{T}]=XY^{T}- YX^{T}- YX^{.

The maximal Bochner-Riesz commutator is defined by B δ, ∗ b ( f ) ( x ) = sup t > 0 | B δ, t b ( f ) ( x ) |.

The commutator ([b, T]) is defined as [b,T]f=bT f -T(bf).

Since the commutator-associator filtration is defined in terms of words (namely, commutators, associators and associator deviations, which are defined in Sect. 8.1, and their compositions) nilpotent loops of class (n) form a variety.

Then the commutator between A and b is defined by [ b, A ] f ( x ) : = b ( x ) A f ( x ) − A ( b f ) ( x ).

It is well known that the commutator [ b, T ] is defined by [ b, T ] ( f ) = T ( b f ) − b T ( f ), where T is a Calderón-Zygmund operator and b ∈ BMO.

The commutator related to T δ is defined by T δ b ( f ) ( x ) = ∫ R n ( b ( x ) − b ( y ) ) K ( x, y ) f ( y ) d y.

The commutator of the maximal operator is defined by M b ( f ) ( x ) = sup t > 0 | B ( x, t ) | − 1 ∫ B ( x, t ) | b ( x ) − b ( y ) | | f ( y ) | d y.

The commutator of (mathcal{I}_{beta}^{L}) is defined by begin{aligned} bigl[b,mathcal{I}_{beta}^{L} bigr]f(x)=b(x) mathcal{I}_{beta}^{L} f(x -mathcal{I}_{beta}^{L}(bf) (x -mathcal{

The commutator operator [ T ˜, b ] is defined by [ T ˜, b ] f ( x ) = b ( x ) T ˜ f ( x ) − T ˜ ( b f ) ( x ).