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Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds
In this paper we prove Nikolskii's inequality on general compact Lie groups and on compact homogeneous spaces with the constant interpreted in terms of the eigenvalue counting function of theExpand
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A Sharp Remez Inequality for Trigonometric Polynomials
AbstractWe obtain a sharp Remez inequality for the trigonometric polynomial Tn of degree n on [0,2π): $$\|T_n \|_{L_\infty([0,2\pi))} \le \biggl(1+2\tan^2 \frac{n\beta}{4m} \biggr) { \|T_nExpand
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Convolution Inequalities in Lorentz Spaces
In this paper we study boundedness of the convolution operator in different Lorentz spaces. We obtain the limit case of the Young-O’Neil inequality in the classical Lorentz spaces. We alsoExpand
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Nikolskii inequality and functional classes on compact lie groups
In this note we study the Besov, Triebel—Lizorkin, Wiener, and Beurling function spaces on compact Lie groups. A major role in the analysis is played by the Nikolskii inequality.
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Weighted Norm Inequalities for Convolution and Riesz Potential
In this paper, we prove analogues of O’Neil’s inequalities for the convolution in the weighted Lebesgue spaces. We also establish the weighted two-sided norm inequalities for the potential operator.
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Norm inequalities for convolution operators
Abstract We study norm convolution inequalities in Lebesgue and Lorentz spaces. First, we improve the well-known O'Neil's inequality for the convolution operators and prove corresponding estimateExpand
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Description of interpolation spaces for local Morrey-type spaces
We consider the real interpolation method and prove that for local Morrey spaces, in the case when they have the same integrability parameter, the interpolation spaces are again local Morrey-typeExpand
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On the coefficients of multiple Fourier series in L_p-spaces
In this paper we use new function spaces and interpolation methods to study the dependence of the properties of summable multiple Fourier series on their coefficients. We obtain theorems for multipleExpand
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