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Hardy, Hardy-Sobolev, Hardy-Littlewood-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights forExpand
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Critical Sobolev, Gagliardo-Nirenberg, Trudinger and Brezis-Gallouet-Wainger inequalities, best constants, and ground states on graded groups
In this paper we investigate critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities associated with the positive Rockland operators on graded groups, which includes theExpand
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Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature
In this paper we obtain Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities with sharp constants on Riemannian manifolds with non-positive sectional curvature and, inExpand
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Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for ^{}-weighted Hardy inequalities
In this paper we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities: we show that for $1<p,q<\infty$, $0<r<\infty$ with $p+q\geq r$,Expand
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Hypoelliptic functional inequalities
In this paper we derive a variety of functional inequalities for general homogeneous invariant hypoelliptic differential operators on nilpotent Lie groups. The obtained inequalities include Hardy,Expand
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Very weak solutions to hypoelliptic wave equations.
In this paper we study the Cauchy problem for the wave equations for hypoelliptic homogeneous left-invariant operators on graded Lie groups when the time-dependent non-negative propagation speed isExpand
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BOUNDARY-VALUE PROBLEMS FOR WAVE EQUATIONS WITH DATA ON THE WHOLE BOUNDARY
In this article we propose a new formulation of boundary-value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. WeExpand
Euler semigroup, Hardy–Sobolev and Gagliardo–Nirenberg type inequalities on homogeneous groups
In this paper we describe the Euler semigroup $$\{e^{-t\mathbb {E}^{*}\mathbb {E}}\}_{t>0}$$ { e - t E ∗ E } t > 0 on homogeneous Lie groups, which allows us to obtain various types of theExpand
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Hardy, Hardy-Sobolev and Caffarelli-Kohn-Nirenberg inequalities on general Lie groups
In this paper we obtain two-weight Hardy inequalities on general metric measure spaces possessing polar decompositions. Moreover, we also find necessary and sufficient conditions for the weights forExpand
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Limiting cases of Sobolev inequalities on stratified groups
In this paper we present critical Gagliardo-Nirenberg, Trudinger-type and Brezis-Gallouet-Wainger inequalities concerning the limiting cases of the embedding theorems for Sobolev spaces on stratifiedExpand
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