• Title/Summary/Keyword: q-Hardy's inequalities

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ON HARDY AND PÓLYA-KNOPP'S INEQUALITIES

  • Kwon, Ern Gun;Jo, Min Ju
    • Journal of the Chungcheong Mathematical Society
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    • v.31 no.2
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    • pp.231-237
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    • 2018
  • Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

A New Dual Hardy-Hilbert's Inequality with some Parameters and its Reverse

  • Zhong, Wuyi
    • Kyungpook Mathematical Journal
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    • v.49 no.3
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    • pp.493-506
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    • 2009
  • By using the improved Euler-Maclaurin summation formula and estimating the weight coefficients in this paper, a new dual Hardy-Hilbert's inequality and its reverse form are obtained, which are all with two pairs of conjugate exponents (p, q); (r, s) and a independent parameter ${\lambda}$. In addition, some equivalent forms of the inequalities are considered. We also prove that the constant factors in the new inequalities are all the best possible. As a particular case of our results, we obtain the reverse form of a famous Hardy-Hilbert's inequality.

WEIGHTED LEBESGUE NORM INEQUALITIES FOR CERTAIN CLASSES OF OPERATORS

  • Song, Hi Ja
    • Korean Journal of Mathematics
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    • v.14 no.2
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    • pp.137-160
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    • 2006
  • We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

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A NOTE ON SOBOLEV TYPE TRACE INEQUALITIES FOR s-HARMONIC EXTENSIONS

  • Yongrui Tang;Shujuan Zhou
    • Journal of the Korean Mathematical Society
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    • v.61 no.2
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    • pp.341-356
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    • 2024
  • In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.