We demonstrate a new light trapping technique that exploits dielectric core-shell optical antennas to strongly enhance solar absorption. This approach can allow the thickness of active materials in solar cells lowered by almost 1 order of magnitude without scarifying solar absorption capability. For example, it can enable a 70 nm thick hydrogenated amorphous silicon (a-Si:H) thin film to absorb 90% of incident solar radiation above the bandgap, which would otherwise require a thickness of 400 nm in typical antireflective coated thin films. This strong enhancement arises from a controlled optical antenna effect in patterned core-shell nanostructures that consist of absorbing semiconductors and nonabsorbing dielectric materials. This core-shell optical antenna benefits from a multiplication of enhancements contributed by leaky mode resonances (LMRs) in the semiconductor part and antireflection effects in the dielectric part. We investigate the fundamental mechanism for this enhancement multiplication and demonstrate that the size ratio of the semiconductor and the dielectric parts in the core-shell structure is key for optimizing the enhancement. By enabling strong solar absorption enhancement, this approach holds promise for cost reduction and efficiency improvement of solar conversion devices, including solar cells and solar-to-fuel systems. It can generally apply to a wide range of inorganic and organic active materials. This dielectric core-shell antenna can also find applications in other photonic devices such as photodetectors, sensors, and solid-state lighting diodes.