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The limit obtained depends on the model used: if the massive photon is described by Proca theory, the experimental upper bound for its mass is about 10−57 grams; if photon mass is generated by a Higgs mechanism, the experimental upper limit is less sharp, m ≤ 10−14 eV/c2 (roughly 2 × 10−47 g).
Both Ms Sharp and Ms Thacker were interviewed by the inquiry team as part of its work for Professor Alexis Jay, who on Tuesday published a report that said at least 1,400 children were sexually exploited from 1997-2013.
Similarly, for a locally L s -integrable form u ( y ), we define the sharp maximal operator M s # by M s # ( u ) = M s # ( u ) ( x ) = sup r > 0 ( 1 | B ( x, r ) | ∫ B ( x, r ) | u ( y ) − u B ( x, r ) | s d y ) 1 s.
While the Committee on Terminology differs between spikes (<70 <span class="lh lhl">ms) and sharp waves (<200 <span class="lh lhl">ms), we agree with Walczak and colleagues (2008) that the clinical utility of this differentiation is uncertain, in particular, in the present context.
The sharp maximal operator M ♯ is defined by M ♯ ( f ) ( x ) = sup Q ∋ x 1 | Q | ∫ Q | f ( y ) − f Q | d y ∼ sup Q ∋ x inf a ∈ C 1 | Q | ∫ Q | f ( y ) − a | d y, where f Q = 1 | Q | ∫ Q f ( x ) d x.
On the other hand, a similar problem connected with the Markov Bernstein inequality has been analyzed in [13] when you try to determine the sharp constant C n, m; w) such that begin{aligned} left| A ^{m/2} P^{(m)}right| _{L^{2}((a,b), w)}le C n,m w) Vert PVert _{L^{2}((a,b), w)},quad text{ for } text{ all } Pin mathbb {P}_{n}.
One can prove directly that the sharp constant B m ( x ) is attainable, i.e., there is a nontrivial y ¯ ∈ W ( 1, 2, m ) such that | y ¯ ( x ) | = B m ( x ) ( ∫ − 1 1 | y ′ ( t ) | 2 d t ) − 1 2. (4.14).
Similarly, the sharp maximal operator M s ♯ is defined by.
The (Hardy-Littlewood) maximal and the sharp maximal functions M f, f p, resp.
Now, we have the following analogy of the classical Fefferman-Stein inequality [[11], Chapter IV] for the sharp maximal function M A ♯ f.
