Necessary and sufficient conditions governing two-weight inequalities with general-type weights for fractional maximal functions and Riesz potentials with variable parameters are established in the lebesguespaces wit...
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Necessary and sufficient conditions governing two-weight inequalities with general-type weights for fractional maximal functions and Riesz potentials with variable parameters are established in the lebesgue spaces with variable exponent. In two-weight inequalities the right-hand side weight to the certain power satisfies the reverse doubling condition. In particular, from the general results we have: generalization of the Sobolev inequality for potentials;criteria governing the trace inequality for fractional maximal functions and potential operators;theorem of Muckenhoupt-Wheeden type ( one-weight inequality) for fractional maximal functions defined on a bounded interval when the parameter satisfies the Dini-Lipschitz condition. Sawyer-type two-weight criteria for fractional maximal functions are also derived.
Necessary and sufficient conditions on a weight pair (v, w) guaranteeing the boundedness of generalized maximal functions and potentials on the half-space from [image omitted] to [image omitted] are found, provided th...
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Necessary and sufficient conditions on a weight pair (v, w) guaranteeing the boundedness of generalized maximal functions and potentials on the half-space from [image omitted] to [image omitted] are found, provided that p is a constant, and w-p' satisfies the dyadic reverse doubling condition. Carleson-type criteria governing the trace inequality for generalized fractional maximal functions and potentials on the half-space are also derived. For fractional maximal functions, we use the technique of dyadic cubes and Carleson-Hormander inequality, while the proofs for fractional integrals rely on the Welland-type inequality. In the diagonal case our conditions are of Sawyer type. The results are new even for constant exponents of lebesguespaces.
Boundedness of one-sided maximal functions, singular integrals and potentials is established in L-p(x)(I) spaces, where I is an interval in R. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
Boundedness of one-sided maximal functions, singular integrals and potentials is established in L-p(x)(I) spaces, where I is an interval in R. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim
We consider the Hardy-Littlewood maximal operator M on Musielak-Orlicz spaces L-phi(R-d). We give a necessary condition for the continuity of M on L-phi(Rd) which generalizes the concept of Muckenhoupt classes. In the...
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We consider the Hardy-Littlewood maximal operator M on Musielak-Orlicz spaces L-phi(R-d). We give a necessary condition for the continuity of M on L-phi(Rd) which generalizes the concept of Muckenhoupt classes. In the special case of generalized lebesguespaces L-P(.)(R-d) we show that this condition is also sufficient. Moreover, we show that the condition is "left-open" in the sense that not only M but also M-q is continuous for some q > 1, where M-q f = (M(vertical bar f vertical bar(q))) (l/q). (c) 2005 Elsevier SAS. All rights reserved.
In this paper we derive weight inequalities for one-sided and Riesz potentials in L-p(x) spaces under the condition that p satisfies a weak Lipschitz condition. Compactness of these operators in L-p(x) spaces is also ...
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In this paper we derive weight inequalities for one-sided and Riesz potentials in L-p(x) spaces under the condition that p satisfies a weak Lipschitz condition. Compactness of these operators in L-p(x) spaces is also established.
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