In this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q >= 2 be the homogeneous dimension of G and Ia denote the Riesz potential of order a on G. Then, for every alpha is an element of (0, Q), there exists a constant C = C(alpha, Q) > 0 such that parallel to I(alpha)f parallel to L-Q/(Q-alpha),L-1(G) <= C parallel to XI(1)f parallel to(L1(G)) (0.1) for all f is an element of C-c(infinity) (G) such that XI(1)f is an element of L-1(G), where X denotes the horizontal gradient.

Some remarks on L-1 embeddings in the subelliptic setting / S.G. Krantz, M.M. Peloso, D. Spector. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 202(2021), pp. 112149.1-112149.11. [10.1016/j.na.2020.112149]

Some remarks on L-1 embeddings in the subelliptic setting

M.M. Peloso
;
2021

Abstract

In this paper we establish an optimal Lorentz estimate for the Riesz potential in the L1 regime in the setting of a stratified group G: Let Q >= 2 be the homogeneous dimension of G and Ia denote the Riesz potential of order a on G. Then, for every alpha is an element of (0, Q), there exists a constant C = C(alpha, Q) > 0 such that parallel to I(alpha)f parallel to L-Q/(Q-alpha),L-1(G) <= C parallel to XI(1)f parallel to(L1(G)) (0.1) for all f is an element of C-c(infinity) (G) such that XI(1)f is an element of L-1(G), where X denotes the horizontal gradient.
Sobolev embeddings; Lorentz spaces; L-1 regime; Stratified group; Subelliptic estimates
Settore MAT/05 - Analisi Matematica
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/777295
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