Mapping properties of the discrete fractional maximal operator in metric measure spaces

DOI10.1215/21562261-2265932zbMath1280.42012OpenAlexW2026785649WikidataQ109992655 ScholiaQ109992655MaRDI QIDQ371230

Toni Heikkinen, Juho Nuutinen, Juha Kinnunen, Heli Tuominen

Publication date: 30 September 2013

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.kjm/1376917630

zbMATH Keywords

Sobolev spaceHölder continuitydoubling measureCampanato spaceMorrey spaceCoifman-Rochberg lemmafractional maximal function

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60)

Related Items

Characterization of the boundedness of fractional maximal operator and its commutators in Orlicz and generalized Orlicz-Morrey spaces on spaces of homogeneous type, Non-local Gehring lemmas in spaces of homogeneous type and applications, Fractional maximal functions and mean oscillation on bounded doubling metric measure spaces, Commutators of fractional maximal operator in variable Lebesgue spaces over bounded quasi‐metric measure spaces, Regularity of fractional maximal functions through Fourier multipliers, Fractional maximal functions in metric measure spaces, Regularity of the local fractional maximal function, Morrey-Sobolev spaces on metric measure spaces, Mapping properties of multilinear fractional maximal operators in metric measure spaces, Mapping properties of maximal operators on infinite connected graphs

Cites Work

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• The discrete maximal operator in metric spaces
• Nonlinear potential theory on metric spaces
• Morrey spaces in harmonic analysis
• Sobolev's inequality for Riesz potentials of functions in non-doubling Morrey spaces
• Lipschitz functions on spaces of homogeneous type
• A decomposition into atoms of distributions on spaces of homogeneous type
• A note on Riesz potentials
• Lebesgue points for Sobolev functions on metric spaces.
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Bounded functions of vanishing mean oscillation on compact metric spaces
• On fractional differentiation and integration on spaces of homogeneous type
• Singular and fractional integral operators on Campanato spaces with variable growth conditions
• Pointwise behaviour of \(M^{1,1}\) Sobolev functions
• The Poincaré inequality is an open ended condition
• Limiting case of the boundedness of fractional integral operators on nonhomogeneous space
• Morrey spaces for non-doubling measures
• On the theory of \({\mathcal L}_{p, \lambda}\) spaces
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Sharp estimates of the modified Hardy-Littlewood maximal operator on the nonhomogeneous space via covering lemmas
• Boundedness of the fractional maximal operator on variable exponent Lebesgue spaces: a short proof
• The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
• Another Characterization of BMO
• Morrey Spaces on Spaces of Homogeneous Type and Estimates for □_b and the Cauchy‐Szegö Projection
• REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION
• Mean Oscillation Over Cubes and Holder Continuity
• Harmonic functions on metric spaces