In this paper, we obtain the
$H_{α,β}f(x_1,x_2): = \mathit{\rm{p.\,v.}}∈\int_{ - \infty }^\infty {} f(x_1-t,x_2-u_1(x_1)[t]^α-u_2(x_1)[t]^β)\,\frac{\textrm{d}t}{t}$
with the bounds are independent of the measurable function
$\mathcal{C}_{α,β}f(x):=\mathop {\sup }\limits_{{N_1},{N_2} \in \mathbb{R}} |{\rm{p.\,v.}}\int_{ - \infty }^\infty {} e^{iN_1[t]^α+iN_2[t]^β}f(x-t)\,\frac{\textrm{d}t}{t}|,$
where
Citation: |
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