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By a simple calculations, we prove that |f|_{L^{p,q}_{beta}(mathbb {R}^{d+1}_^{q} = pint_{0}^{infty}lambda^{q} bigl(d_{f,beta}(lambda bigr)^{frac{q}{p}} frac{dlambda}{lambda}, quad mbox{if } q < infty.
Such a simulation-based technique is required because, when hardware resources are considered, it is important to look beyond a simple calculations that determine whether or not enough resources are available.
(2.16) By a simple calculations we see that, for almost all (xin mathbb {R}^{d}_), int_{0}^{infty}big|mathcal{F}_{W}(h) (lambda x big|^{2}frac{dlambda}{lambda} < infty.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com