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For each, we obtain sharp or nearly sharp ranges of p using the general theory for boundedness of Part I and the off-diagonal estimates of Part II.
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Both the TRAID Remade label and Clic Sargent's Fix Up Look Sharp range sell original upcycled designs.
The sharp range of estimates for the resulting operator is obtained in all dimensions, except for an endpoint.
We are hence able to obtain a sharp range of admissible Sobolev exponents for which the spacetime estimate holds.
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents.
We find the sharp range of boundedness for transplantation operators associated with Laguerre function expansions in Lp spaces with power weights.
And with columnists including Charlie Brooker, Jacques Peretti, Grace Dent, Joe Queenan and Jonathan Bernstein, it has the sharpest range of voices of any weekend culture guide.
Characterizing western areas heavily exposed to Atlantic air masses, the maritime type of climate given the latitudinal stretch of those lands exhibits sharp temperature ranges.
Now 81, William King, a sculptor-gadfly whose spare, sharp figures range from monumental to tabletop in size, still exempts nobody -- including himself -- from his satire.
Pat Richards, for instance, is coming to the end of a seven-season stint on the wing for Wigan, for whom he has won countless matches with his metronomic goal-kicking and sharp, close-range finishing.
Often compared to Monte Zoncolan in Italy, the Angliru was unknown before 1996 when a member of a Spanish cycling team decided to check out rumours of a super-steep climb hidden away in the Picos de Europa, the razor sharp mountain range that isolates the Asturias region from the rest of Spain.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com